Strong convergence rates for full-discrete approximations of stochastic Burgers equations with multiplicative noise

TL;DR

This paper proves strong convergence rates for explicit full-discrete numerical schemes approximating stochastic Burgers equations with multiplicative noise, using uniform exponential moment estimates.

Contribution

It introduces a novel approach to establish strong convergence rates for full-discrete schemes of stochastic Burgers equations with multiplicative noise.

Findings

Established strong convergence rates on the entire probability space.

Derived uniform exponential moment estimates for numerical approximations.

Validated the effectiveness of the proposed numerical schemes.

Abstract

In this article we establish strong convergence rates on the whole probability space for explicit full-discrete approximations of stochastic Burgers equations with multiplicative trace-class noise. The key step in our proof is to establish uniform exponential moment estimates for the numerical approximations.