Analysis of an exponential integrator for stochastic PDEs driven by Riesz noise

TL;DR

This paper introduces and analyzes an explicit exponential integrator for stochastic partial differential equations driven by Riesz noise, providing theoretical error bounds and numerical validation in 1D and 2D.

Contribution

The paper develops a new exponential integrator for SPDEs with Riesz noise and establishes convergence rates depending on the Riesz kernel exponent.

Findings

Proven strong error bounds for the integrator.

Convergence rate depends on Riesz kernel exponent.

Numerical experiments confirm theoretical results.

Abstract

We present and study an explicit exponential integrator for parabolic SPDEs in any dimension driven by a Gaussian noise which is white in time and with spatial correlation given by a Riesz kernel. Under assumptions on the coefficients of the SPDE, we prove strong error bounds and exhibit how the rate of convergence depends on the exponent in the Riesz kernel. Finally, numerical experiments in spatial dimensions $1$ and $2$ are provided in order to confirm our convergence results.