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?