Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $\alpha$-stable additive noise

TL;DR

This paper establishes the weak convergence rate of the Euler-Maruyama scheme for density-dependent SDEs driven by $oldsymbol{ extit{ extalpha}}$-stable noise, providing explicit total variation bounds for the approximation.

Contribution

It introduces an explicit convergence rate in total variation for Euler-Maruyama applied to $ extalpha$-stable driven SDEs with density dependence, extending previous well-posedness results.

Findings

Derived explicit convergence rate in total variation

Applied technique from Hao (2023) for analysis

Extended results to $ extalpha$-stable noise with $ extalpha extin(1,2)$

Abstract

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\alpha$-stable processes with $\alpha\in(1,2)$. The well-posedness of these equations has been previously obtained in \cite{wu2023well}. We derive an explicit convergence rate in total variation for the Euler-Maruyama scheme, employing a technique rooted in \cite{hao2023}.