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