Stochastic Parabolic Equations of Full Second Order
Lototsky, S. V.
Rozovskii, B. L.
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.
Mathematics - Probability, Mathematics - Analysis of PDEs, 60H15, 35R60, 60H40