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Stochastic Taylor Expansions

• To: mathgroup at smc.vnet.net
• Subject: [mg2502] Stochastic Taylor Expansions
• From: Amir Khosrowshahi <khosra at fi.gs.com>
• Date: Wed, 15 Nov 1995 01:59:24 -0500
• Organization: Goldman, Sachs & Co

Hi,

Was wondering if anyone has taken a look at symbolic ito-taylor
expansions in mathematica. The idea is to take the ordinary ito integral
and expand it into a bunch of multiple wiener intergrals with constant
integrands plus a remainder term, analogous to the deterministic taylor
expansion. It is easy to define the expansion recursively in
mathematica. I would like to stick the expansion into the Feynmann-Kac
formula in the end and try to get first, second order analytic
expressions for the solutions (assuming weak convergence, etc.) I think
this is analogous to getting perturbative expansions of path integrals
in field theory.

I would appreciate any direction or advice.

Also, does anybody know how to calculate moments of multiple stochastic
integrals?