On the rate of convergence of simple and jump-adapted weak Euler schemes for Levy driven SDEs

TL;DR

This paper analyzes the convergence rates of weak Euler schemes for Levy-driven SDEs, focusing on how coefficient regularity and increment approximation affect convergence, including jump-adapted schemes.

Contribution

It provides new theoretical results on convergence rates for both exact and approximate Euler schemes applied to Levy-driven SDEs with Hölder-continuous coefficients.

Findings

Derived convergence rates for weak Euler schemes with Levy processes.

Established robustness of convergence rates to increment approximation.

Extended analysis to jump-adapted schemes with similar convergence properties.

Abstract

The paper studies the rate of convergence of the weak Euler approximation for solutions to possibly completely degenerate SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and driving processes. In addition, the rate robustness to the approximation of the increments of the driving process is studied and approximate Euler scheme considered. A rate of convergence is derived for an approximate jump-adapted scheme as well.