On the rate of convergence of weak Euler approximation for non-degenerate SDEs

TL;DR

This paper analyzes how quickly the weak Euler approximation converges for non-degenerate SDEs with Hölder continuous coefficients driven by jump processes, including Levy processes and diffusions.

Contribution

It provides new estimates for the convergence rate of the weak Euler scheme for a broad class of non-degenerate SDEs with jumps and Hölder continuous coefficients.

Findings

Derived convergence rate estimates for the weak Euler approximation.

Applicable to SDEs driven by Levy processes and diffusions.

Includes cases with non-degenerate main parts and absolutely continuous jump measures.

Abstract

The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose jump intensity measure is absolutely continuous with respect to the Levy measure of a spherically-symmetric stable process. It includes the nondegenerate diffusions and SDEs driven by Levy processes.