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

2024/05/31 by Song Ke, Song, Ke, Zimo Hao +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2405.20840

openalex publication_date 2024/05/31 · openalex created_date 2024/06/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by α-stable processes with α∈(1,2). The well-posedness of these equations has been previously obtained in \citewu2023well. We derive an explicit convergence rate in total variation for the Euler-Maruyama scheme, employing a technique rooted in \citehao2023.

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