Almost sure approximation of Wong-Zakai type for stochastic partial differential equations

A solution to a stochastic partial differential equation (in the Stratonovitch form) is an almost sure limit of solutions to a sequence of approximated equations (with Brownian path w(t) being replaced by a piecewise smooth path wn(t) approximating w(t)). This is achieved by employing a generalized Feynman-Kac formula of Pardoux and Rozovskii and proving the corresponding result for ordinary stochastic differential equations. Parabolic and hyperbolic (degenerate parabolic) evolution equations are studied.