Stabilization of Distribution Dependent Stochastic Differential Equations Driven by Lévy Noise with Discrete-Time Feedback Controls

Guangjun Shen (), Jie Song (), Jiang-Lun Wu () and Xiuwei Yin ()
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Guangjun Shen: Anhui Normal University
Jie Song: Anhui Normal University
Jiang-Lun Wu: BNBU
Xiuwei Yin: Anhui Normal University

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-27

Abstract: Abstract Due to the intrinsic link with (kinetic) nonlinear Fokker–Planck equations and many profound and diverse applications, distribution dependent stochastic differential equations have been investigated intensively in recent years. In this paper, we aim to derive the mean square exponential stabilization of the distribution dependent stochastic differential equations driven by Lévy noise via feedback controls based on discrete-time state observations. To this end, we first present sufficient conditions to ensure the existence and uniqueness of solutions of the concerned equations. Then, we design a discrete-time feedback control in the drift part and obtain the mean square exponential stability for the controlled systems. Finally, we give an example to illustrate our theoretical results.

Keywords: Distribution dependent stochastic differential equations; Lévy noise; Mean square exponential stability; Discrete-time feedback control; 60H10; 93D15; 60G51 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01448-3

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