create new finite-state Markov chain
MarkovChain(P, S, i, n)
Matrix; transition matrix
Vector; state space
posint; initial state
posint; number of states per year
The MarkovChain command creates a new finite state Markov chain.
The parameter P is the transition matrix; it must be a square matrix (see Matrix) of size d, where d is the number of states in the Markov chain. The value Pi,j defines the probability of moving from state j to state i.
The parameter S is a vector containing values for all possible states of the process.
The parameter n is the number of states per year. This process can only be simulated with m=n⁢k time steps per year, where k is a positive integer. Assume for example that X is a finite state Markov chain with 3 states per year. If we simulate the process X on the interval 0..2 with 12 time steps, then the state change can occur only at steps 2, 4, 6, 8, and 10.
P := <<0.5, 0.5>|<0.2, 0.8>>;
X := MarkovChain(P, <1.0, 2.0>, 1, 5);
SamplePath(X(t), t = 0..2, timesteps = 10, replications = 10);
The following command will issue an error because the number of time steps used in simulation must be a multiple of the number of states per year.
SamplePath(X(t), t = 0..2, timesteps = 12, replications = 10);
Error, (in Finance:-SamplePath) update time .200000000000000011 does not belong to the time grid
The Finance[MarkovChain] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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