Rate of convergence of Wong-Zakai approximations for stochastic partial differential equations

TL;DR

This paper establishes that the convergence rate of Wong-Zakai approximations for stochastic PDEs driven by Wiener processes matches the convergence rate of the approximating processes, given the convergence of their area processes.

Contribution

It demonstrates the convergence rate equivalence for Wong-Zakai approximations in stochastic PDEs, including cases with time-dependent coefficients and degeneracy.

Findings

Convergence rate of Wong-Zakai approximations matches that of the driving processes.

Area process convergence is essential for the approximation rate.

Applicable to both non-degenerate and degenerate stochastic PDEs.

Abstract

In this paper we show that the rate of convergence of Wong-Zakai approximations for stochastic partial differential equations driven by Wiener processes is essentially the same as the rate of convergence of the driving processes W_n approximating the Wiener process, provided the area processes of W_n also converge to those of W with that rate. We consider non-degenerate and also degenerate stochastic PDEs with time dependent coefficients.