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

Song, Ke; Hao, Zimo

doi:10.1090/proc/17169

Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $\alpha$-stable additive noise
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by Ke Song and Zimo Hao;

Proc. Amer. Math. Soc. 153 (2025), 2591-2607

DOI: https://doi.org/10.1090/proc/17169

Published electronically: March 26, 2025

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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 Wu and Hao [Stochastic Process. Appl. 164 (2023), pp. 416–442]. We derive an explicit convergence rate in total variation for the Euler-Maruyama scheme, employing a technique rooted in Hao [McKean-Vlasov SDEs with singular drifts, Thesis (Ph.D.), Bielefeld: Universitatät Bielefeld; 2023].

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Proceedings of the American Mathematical Society

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