create new Wiener process
(optional) stochastic process with non-negative increments, or a deterministic function of time; subordinator
Matrix; covariance matrix
The WienerProcess command creates a new Wiener process. If called with no arguments, the WienerProcess command creates a new standard Wiener process, W⁡t, that is a Gaussian process with independent increments such that W⁡0=0 with probability 1, E⁡W⁡t=0 and Var⁡W⁡t−W⁡s=t−s for all 0≤s≤t.
The WienerProcess(Sigma) calling sequence creates a Wiener process with covariance matrix Sigma. The matrix Sigma must be a positive semi-definite square matrix. The dimension of the generated process will be equal to the dimension of the matrix Sigma.
If an optional parameter J is passed, the WienerProcess command creates a process of the form W⁡J⁡t, where W⁡t is the standard Wiener process. Note that the subordinator J⁡t must be an increasing process with non-negative, homogeneous, and independent increments. This can be either another stochastic process such as a Poisson process or a Gamma process, a procedure, or an algebraic expression.
First create a standard Wiener process and generate 50 replications of the sample path and plot the result.
Define another stochastic variable as an expression involving W1. You can compute the expected value of X⁡3 using Monte Carlo simulation with the specified number of replications of the sample path.
Define another stochastic variable Y, which also depends on W1 but uses symbolic coefficients. Note that Y is an Ito process, so it is governed by the stochastic differential equation (SDE) dY⁡t=μ⁡Y⁡t,t⁢dt+σ⁡Y⁡t,t⁢dW⁡t. You can use the Drift and Diffusion commands to compute μ and σ.
Create a subordinated Wiener process that uses a Poisson process with intensity parameter λ=0.3 as subordinator.
Here is a representation of the Ornstein-Uhlenbeck process in terms of or a subordinated Wiener process. In this case the subordinator is a deterministic process that can be specified as a Maple procedure or an algebraic expression.
The Finance[WienerProcess] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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