Euler-Maruyama scheme for SDE driven by L\'evy process with H\"older drift

TL;DR

This paper analyzes the Euler-Maruyama numerical scheme for stochastic differential equations driven by Lévy processes with Hölder continuous drifts, providing error estimates applicable to various stable processes.

Contribution

It derives $L^p$-error bounds for the Euler-Maruyama scheme in SDEs driven by Lévy processes with Hölder drifts, covering a wide class of stable noises.

Findings

Error bounds for Euler-Maruyama scheme derived

Applicable to all nondegenerate $eta$-stable processes

Enhanced understanding of numerical approximation for Lévy-driven SDEs

Abstract

This study focuses on approximating solutions to SDEs driven by L\'evy processes with H\"older continuous drifts using the Euler-Maruyama scheme. We derive the $L^p$-error for a broad range of driven noises, including all nondegenerate $\alpha$-stable processes ($0<\alpha<2$).