Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with jumps and irregular drift coefficient

Abstract

In this paper, we consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations (SDEs) with càdlàg process. We provide the strong rate of convergence when the drift coefficient is the sum of a Lipschitz continuous function and a monotone decreasing Hölder continuous function. We also prove the pathwise uniqueness and the existence for SDEs.