Stochastic boundary value problems: a white noise functional approach

Abstract

We give a program for solving stochastic boundary value problems involving functionals of (multiparameter) white noise. As an example we solve the stochastic Schrödinger equation {ie391-1} where V is a positive, noisy potential. We represent the potential V by a white noise functional and interpret the product of the two distribution valued processes V and u as a Wick product V {lozenge, open}u. Such an interpretation is in accordance with the usual interpretation of a white noise product in ordinary stochastic differential equations. The solution u will not be a generalized white noise functional but can be represented as an L1 functional process. © 1993 Springer-Verlag.