A Wong-Zakai theorem for stochastic PDEs

TL;DR

This paper establishes a Wong-Zakai theorem for one-dimensional parabolic nonlinear stochastic PDEs driven by space-time white noise, providing a detailed local description of solutions and extending classical results to stochastic PDEs.

Contribution

It introduces a Wong-Zakai type approximation theorem for nonlinear stochastic PDEs driven by space-time white noise, a significant extension of existing results.

Findings

Proves a Wong-Zakai theorem for specific stochastic PDEs.

Provides a detailed local description of solutions.

Extends classical Wong-Zakai results to stochastic PDEs.

Abstract

We prove a version of the Wong-Zakai theorem for one-dimensional parabolic nonlinear stochastic PDEs driven by space-time white noise. As a corollary, we obtain a detailed local description of solutions. Dedicated to the memory of Kiyosi It\^o on the occasion of the 100th anniversary of his birth.