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Stochastic Taylor Expansions
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?