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Research Article | Open Access

Almost automorphic solutions for mean-field SDEs driven by Lévy noise

Xin Liu( ), Yongqi Hou
School of Science, Dalian Maritime University, Dalian 116026, China
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Abstract

The paper is dedicated to studying the almost automorphic solutions for mean-field SDEs with Lévy noise. It is proven that if the coefficients satisfy the Lipschitz conditions, the equation admits a unique bounded solution, and the solution can inherit in distribution the almost automorphy of the coefficients. In addition, we investigate the global asymptotic stability of these solutions. We also give an example of the stochastic heat equation to illustrate our work.

Keywords

almost automorphymean-field stochastic differential equationsLévy processasymptotic stability
CLC number: 34C27, 34G20, 60G51, 60H10

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AIMS Mathematics
Volume 10 Issue 5,
May 2025
Pages 11159-11183
DOI: 10.3934/math.2025506

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Cite this article:
Liu X, Hou Y. Almost automorphic solutions for mean-field SDEs driven by Lévy noise. AIMS Mathematics, 2025, 10(5): 11159-11183. https://doi.org/10.3934/math.2025506

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Received: 23 February 2025
Revised: 14 April 2025
Accepted: 08 May 2025
Published: 15 May 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)