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Re: Stochastic differential equations

• To: mathgroup at smc.vnet.net
• Subject: [mg25362] Re: Stochastic differential equations
• From: Mark Fisher <fisherlink at earthlink.net>
• Date: Sun, 24 Sep 2000 03:01:30 -0400 (EDT)
• References: <8qhoil$jj4@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Emily, 

At my website is a package ItosLemma.m that implements Ito's lemma in
Mathematica. (There is also a notebook ItosLemma.nb with some guidance for
usage.) 

http://www.markfisher.net/~mefisher/mma/mathematica.html

I use it all the time. There are two "drawbacks" in using the package.
First, the package uses a number of "global" variables. To make them
user-friendly, I put the following in my init.m file:

{TimeSymbol, TimeIncrement, BrownianIncrement, CorrelationSymbol,
DriftSymbol, DiffusionSymbol} = 
	{t, dt, dB, \[Rho], \[Mu], \[Sigma]}

The second drawback is that you have to "decare" an Ito process before
it is recognized as such. For example, to declare the process x to have
drift m and diffusion s, (i.e., dx = m dt + s dB) use 

ItoMake[x[t], m, s]

Then, to apply Ito's lemma, use

ItoD[f[x[t],t]]

The package allows multiple Brownians with arbitrary correlation. 

--Mark

mark at markfisher.net

Emily.A.Grimm at sf.frb.org wrote:
> 
> Hi,
> In the 1992 archives, someone asked:
> 
> Has anybody added any facilities for solving stochastic differential equations
> by adding rules like Ito's Lemma to Mathematica ??
> 
> This is my exact question, but I didn't see any offered answers in the
> archive.
> Any ideas?
> 
> Thanks!
> Emily