STOCHASTIC BOUNDARY-VALUE-PROBLEMS - A WHITE-NOISE FUNCTIONAL-APPROACH

We give a program for solving stochastic boundary value problems invol ving functionals of (multiparameter) white noise. As an example we sol ve the stochastic Schrodinger equation DELTAu + V . u = -f in D subset -of R(d), u\partial derivative D = 0 where V is a positive, noisy pote ntial. We represent the potential V by a white noise functional and in terpret the product of the two distribution valued processes V and u a s a Wick product V lozenge u. Such an interpretation is in accordance with the usual interpretation of a white noise product in ordinary sto chastic differential equations. The solution u will not be a generaliz ed white noise functional but can be represented as an L1 functional p rocess.