Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $\hat{I}\pm$-stable additive noise

Abstract

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $\hat{I}\pm$-stable processes with $\hat{I}\pm \in (1,2)$. 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}.