Approximation of SPDEs with Holder Continuous Drifts

TL;DR

This paper studies the strong convergence of exponential integrator schemes for SPDEs with H"older continuous drifts, leveraging Kolmogorov equation regularities to determine convergence rates.

Contribution

It introduces a novel analysis of exponential integrator schemes applied to SPDEs with non-smooth drifts, providing explicit convergence rates.

Findings

Established strong convergence of the scheme for H"older continuous drifts.

Derived explicit convergence rates based on regularity properties.

Extended analysis to a range of stochastic partial differential equations.

Abstract

In this paper, exploiting the regularities of the corresponding Kolmogorov equations involved we investigate strong convergence of exponential integrator scheme for a range of stochastic partial differential equations, in which the drift term is H\"older continuous, and reveal the rate of convergence.