Euler--Maruyama approximation for SDEs with jumps and non-Lipschitz coefficients

Abstract

In this paper we show that stochastic differential equations with jumps and non-Lipschitz coefficients have $(\xi,W,N_{p})$-pathwise unique strong solutions by the Euler--Maruyama approximation. Moreover, the Euler--Maruyama discretisation has an optimal strong convergence rate.