Optimal rate of convergence for approximations of SPDEs with non-regular drift

TL;DR

This paper establishes the optimal convergence rate for a finite difference scheme approximating stochastic reaction-diffusion equations driven by space-time white noise, without requiring regularity assumptions on the reaction term.

Contribution

It proves the optimal strong convergence rate for a fully discrete scheme for SPDEs with non-regular drift using stochastic sewing techniques.

Findings

Optimal strong convergence rate established

Applicable to SPDEs with irregular reaction terms

Uses stochastic sewing method for proof

Abstract

A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the non-linear reaction term. The proof relies on stochastic sewing techniques.