Optimal rate of convergence for stochastic Burgers-type equations

TL;DR

This paper improves the known convergence rate for numerical approximations of one-dimensional stochastic Burgers-type equations with additive noise, establishing an optimal rate close to 1/2.

Contribution

It proves that the convergence rate for additive noise cases is arbitrarily close to 1/2, which is an improvement over the previous 1/6 rate.

Findings

Convergence rate for additive noise is close to 1/2.

Numerical approximations converge in the uniform topology.

Improves previous convergence rate results.

Abstract

Recently, a solution theory for one-dimensional stochastic PDEs of Burgers type driven by space-time white noise was developed. In particular, it was shown that natural numerical approximations of these equations converge and that their convergence rate in the uniform topology is arbitrarily close to $\frac{1}{6}$. In the present article we improve this result in the case of additive noise by proving that the optimal rate of convergence is arbitrarily close to $\frac{1}{2}$.