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Fractional Brownian Motion

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Fractional Brownian Motion 

 

The following was implemented in Maple by Marcus Davidsson (2008) davidsson_marcus@hotmail.com 

with significant help from Dr Aleksandrs Mihailovs 

 

We can  simulate a Fractional Brownian Motion as follows 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(myplot, proc (H) local fBm, t, s, S; `:=`(fBm, proc (H, t) local X, G, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, ...
 

 

 

   Embedded component                       Embedded component 

 

 

 

 

 

If the Hurst Exponent H = .5 then the increments of the process are serial independent (Brownian Motion, Pure Random Walk) 

 

If the Hurst Exponent `>`(H, .5) then the increments of the process are positively serial dependent 

 

If the Hurst Exponent `<`(H, .5) then the increments of the process are negatively serial dependent 

 

 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
 

 

 

Plot_2d
Plot_2d
Plot_2d
 

 

 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
 

 

 

Plot_2d
Plot_2d
Plot_2d
 

 

 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
restart; 1; randomize(); -1; with(Statistics); -1; with(LinearAlgebra); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local G, s, n; `:=`(n, nops(t)); `:=`(G, Matrix(n, proc (i, j) options operator, arro...
 

 

 

Plot_2d
Plot_2d
Plot_2d
 

 

 

 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .7); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
 

Plot_2d
 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 10); -1; `:=`(H, .5); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, ...
 

Plot_2d
 

 

 

 

restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
restart; 1; randomize(); -1; with(Statistics); -1; with(plots); -1; with(LinearAlgebra); -1; `:=`(n, 100); -1; `:=`(nstock, 5); -1; `:=`(H, .3); -1; for k to nstock do `:=`(fBm, proc (H, t) local X, G...
 

Plot_2d
 

 

 

 

restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .7); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
 

Plot_2d
 

 

 

 

 

 

 

restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .5); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
 

Plot_2d
 

 

 

 

 

 

 

restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
restart; 1; randomize(); -1; `:=`(H, .3); -1; `:=`(fBm, proc (H, t) local X, G, s, v, n; `:=`(n, nops(t)); `:=`(X, Statistics:-RandomVariable(Normal(0, 1))); `:=`(G, Matrix(n, proc (i, j) options oper...
 

Plot_2d
 

 

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