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

Ke Song; Zimo Hao

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arXiv · 2405.20840

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

Ke Song·Zimo Hao

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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}.

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Ke Song, Zimo Hao. 2024-05-31. Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $\alpha$-stable additive noise. https://arxiv.org/abs/2405.20840

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