Hellinger and total variation distance in approximating L{\'e}vy driven SDEs

TL;DR

This paper establishes convergence rates in total variation distance for discretized approximations of Lévy-driven SDEs, utilizing Malliavin calculus for jump processes, with a focus on Euler schemes.

Contribution

It provides new convergence rate results in total variation for Lévy-driven SDE approximations using Malliavin calculus techniques.

Findings

Convergence rates in total variation distance are derived.

Results apply to Euler approximation schemes.

Sharp local estimates in Hellinger distance are achieved.

Abstract

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of L{\'e}vy driven stochastic differential equations, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.