Wong–Zakai approximations with convergence rate for stochastic partial differential equations

ABSTRACT

The goal of this paper is to prove a convergence rate for Wong–Zakai approximations of semilinear stochastic partial differential equations driven by a finite-dimensional Brownian motion. Several examples, including the HJMM equation from mathematical finance, illustrate our result.

KEYWORDS:

• Stochastic partial differential equation
• Wong–Zakai approximation
• convergence rate
• graph norm

MATHEMATICS SUBJECT CLASSIFICATION:

• 60H15
• 60G17

Acknowledgment

The authors are grateful to Josef Teichmann for initiating this research topic, and for his invaluable assistance and discussions. The authors also wish to thank Ludwig Baringhaus for his advice regarding the reference [36] used for the calculation of the expectation in Lemma 4.5.

The authors are also grateful to an anonymous referee for valuable comments and suggestions.