Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients

TL;DR

This paper investigates the strong convergence properties of the Euler-Maruyama method when applied to stochastic differential equations with potentially discontinuous drift and diffusion coefficients.

Contribution

It provides new theoretical results on the convergence behavior of Euler-Maruyama for SDEs with discontinuous coefficients, expanding understanding beyond smooth cases.

Findings

Established strong convergence under discontinuous coefficients

Derived convergence rates for the Euler-Maruyama approximation

Extended existing theory to more general SDEs

Abstract

In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.