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Milan
06/15/13 10:36am



While looking in the help manual of Mathematica concerning the ItoProcess function I found the following:

ItoProcess[{a,b,c},x,t]: represents an Ito Process y(t)=c(t,x(t)), where dx(t)=a(t,x(t))dt+b(t,x(t)).dw(t)

In order to replicate and Plot this, I entered the following code:

(*Defining a process y(t)=c((xt)), where \[DifferentialD]x(t)=\[Mu]\
\[DifferentialD]t+\[Sigma]\[DifferentialD]w(t)*)

ItoProcess[\[DifferentialD]x[
t] == \[Mu] \[DifferentialD]t + \[Sigma] \[DifferentialD]w[t],
c[x[t]], {x, 0}, t, w \[Distributed] WienerProcess[]]

Then I wanted to Plot one process by implementing drift and volatility.

(*Simulation of one Ito Process with \[Mu]=0.1 and \[Sigma]=0.2, \
starting value x=0*)

testprocess5 =
ItoProcess[\[DifferentialD]x[t] ==
0.1 *\[DifferentialD]t + 0.2 *\[DifferentialD]w[t],
c[x[t]], {x, 0}, t, w \[Distributed] WienerProcess[]]

Concerning this code I got the same output like in the Mathematica help manual just the drift and the volatility were substituted by 0.1 and 0.2 respectively.

However, when I tried to plot the process it did not work out.

ListLinePlot[
Table[RandomFunction[
testprocess5, {0 (*startis from t=0*), 5 (*ends at t=5*),
0.01 (*\[CapitalDelta]t*)}] ["Path"], {1(*number of paths*)}],
Joined -> True, AxesLabel -> {"time", "value"}, ImageSize -> 400,
PlotRange -> All]

I am not sure, why it is not workling, maybe it could be due to y (t) = c ((xt)). Does anyone of you have a solution for this problem or a suggestion how to change the code?

thanks


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Subject (listing for 'ItoProcess function')
Author Date Posted
ItoProcess function Milan 06/15/13 10:36am
Re: ItoProcess function Bill Simpson 06/20/13 02:41am
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