Convergence of tamed Euler schemes for a class of stochastic evolution equations

TL;DR

This paper demonstrates the stability and convergence of a fully explicit tamed Euler scheme combined with Galerkin spatial discretization for stochastic evolution equations with super-linear drift operators.

Contribution

It introduces a novel application of the tamed Euler method to stochastic evolution equations with super-linear growth, ensuring stability and convergence.

Findings

Proves stability of the discretization scheme.

Establishes convergence of the scheme.

Validates the method for equations with super-linear drift.

Abstract

We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done using the recently developed tamed Euler method, which uses a fully explicit time stepping, coupled with a Galerkin scheme for the spatial discretization.