On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes

R. Mikulevicius; Fanhui Xu

paper

On the rate of convergence of strong Euler approximation for SDEs driven by Levy processes

arXiv:1608.02303

Abstract

SDE driven by an $α$ -stable process, $α \in [1, 2),$ with Lipshitz continuous coefficient and $β$ -Hölder drift is considered. The existence and uniqueness of a strong solution is proved when $β > 1 - α /2$ by showing that it is $L_{p}$ -limit of Euler approximations. The $L_{p}$ -error (rate of convergence) is obtained for a nondegenerate truncated and nontruncated driving process. The rate in the case of Lipshitz continuous coefficients is derived as well.