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

Xin Liu; Yongqi Hou; Xin Liu; Yongqi Hou

doi:10.3934/math.2025506

AIMS Mathematics

2025, Volume 10, Issue 5: 11159-11183. doi: 10.3934/math.2025506

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Research article

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

Xin Liu ^,,
Yongqi Hou

School of Science, Dalian Maritime University, Dalian 116026, China

Received: 23 February 2025 Revised: 14 April 2025 Accepted: 08 May 2025 Published: 15 May 2025
MSC : 34C27, 34G20, 60G51, 60H10

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.
- almost automorphy,
- mean-field stochastic differential equations,
- Lévy process,
- asymptotic stability
Citation: Xin Liu, Yongqi Hou. Almost automorphic solutions for mean-field SDEs driven by Lévy noise[J]. AIMS Mathematics, 2025, 10(5): 11159-11183. doi: 10.3934/math.2025506

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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.

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