English

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

Probability 2024-06-03 v1

Abstract

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by α\alpha-stable processes with α(1,2)\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}.

Keywords

Cite

@article{arxiv.2405.20840,
  title  = {Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $\alpha$-stable additive noise},
  author = {Ke Song and Zimo Hao},
  journal= {arXiv preprint arXiv:2405.20840},
  year   = {2024}
}