Strong convergence rate of Euler-Maruyama approximations in temporal-spatial H\"older-norms for L\'evy-driven stochastic differential equations

TL;DR

This paper analyzes the convergence rate of Euler-Maruyama approximations for Lévy-driven SDEs in H"older norms, providing insights into their accuracy in both time and space.

Contribution

It establishes the strong convergence rate of Euler-Maruyama schemes in H"older norms for Lévy-driven SDEs, a novel analysis in this context.

Findings

Derived explicit convergence rates in H"older norms

Extended analysis to Lévy-driven stochastic differential equations

Provided theoretical bounds for approximation errors

Abstract

We study the error between the exact solution and its Euler-Maruyama approximation in temporal-spatial H\"older-norms for L\'evy-driven stochastic differential equations.