Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

TL;DR

This paper introduces an explicit numerical method for stochastic evolution equations with non-globally Lipschitz nonlinearities, proving strong convergence rates especially for globally monotone coefficients, applicable to stochastic reaction-diffusion PDEs.

Contribution

It presents a new explicit approximation method with proven strong convergence rates for a broad class of stochastic evolution equations with challenging nonlinearities.

Findings

The method achieves strong convergence for equations with globally monotone coefficients.

Applicable to stochastic reaction-diffusion partial differential equations.

Provides explicit, easily implementable numerical scheme.

Abstract

In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong convergence rates for this approximation method in the case of semilinear stochastic evolution equations with globally monotone coefficients. Our strong convergence result, in particular, applies to a class of stochastic reaction-diffusion partial differential equations.