Generalized Brownian functionals and the solution to a stochastic partial differential equation

AbstractA class of generalized Wiener functionals, related to those of Hida and Watanabe, is introduced and the Malliavin calculs associated with these functionals is developed. These notions are applied to the derivation of a solution to the stochastic partial differential equation ∂Y∂t = LY + Y · η + ψ, where L is a second order partial differential operator in the n space variables, η denotes a white noise in the (n + 1) space-time variables, Y · η denotes a Skorohod type stochastic integral, and ψ is a non-random function of the (n + 1) independent variables