Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

TL;DR

This paper proves strong convergence of order 1/2 for the tamed-Euler-Maruyama method applied to SDEs with both discontinuous and polynomially growing drift coefficients, addressing complex irregularities in stochastic differential equations.

Contribution

It combines analysis of irregular coefficients with convergence proof for the tamed-Euler-Maruyama scheme, extending previous results to more challenging SDEs.

Findings

Proves strong convergence of order 1/2 for the scheme.

Addresses SDEs with both discontinuous and polynomially growing drifts.

Extends applicability of the tamed-Euler-Maruyama method.

Abstract

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012].