On the Rate of Convergence of Weak Euler Approximation for Nondegenerate SDEs Driven by Levy Processes

TL;DR

This paper analyzes how quickly the weak Euler approximation converges for nondegenerate SDEs driven by Levy processes, focusing on the influence of coefficient regularity and the stable process's properties.

Contribution

It provides new insights into the convergence rates of weak Euler schemes for Levy-driven SDEs with Hölder-continuous coefficients, considering non-degeneracy and stability.

Findings

Convergence rate depends on coefficient regularity and Levy process stability.

Established bounds for weak Euler approximation errors.

Analyzed the impact of non-degeneracy on convergence speed.

Abstract

The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and driving processes. The equation considered has a non-degenerate main part driven by a spherically-symmetric stable process.