Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control

Guangjun Shen; Xueying Wu; Xiuwei Yin

doi:10.3934/dcdsb.2020133

Article Contents

2021, Volume 26, Issue 2: 755-774. Doi: 10.3934/dcdsb.2020133

This issue Previous Article Next Article Stabilities and dynamic transitions of the Fitzhugh-Nagumo system

Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, China

^* Corresponding author: Guangjun Shen
^* Corresponding author: Guangjun Shen

Received: November 2019

Revised: January 2020

Early access: April 2020

Published: February 2021

This work has been partially supported by the Top talent project of university discipline (specialty) (gxbjZD03), the Distinguished Young Scholars Foundation of Anhui Province (1608085J06), the National Natural Science Foundation of China (11901005)

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Abstract

The stabilization of stochastic differential equations driven by Brownian motion (G-Brownian motion) with discrete-time feedback controls under Lipschitz conditions has been discussed by several authors. In this paper, we first give the sufficient condition for the mean square exponential instability of stochastic differential equations driven by G-Lévy process with non-Lipschitz coefficients. Second, we design a discrete-time feedback control in the drift part and obtain the mean square exponential stability and quasi-sure exponential stability for the controlled systems. At last, we give an example to verify the obtained theory.

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Mathematics Subject Classification: 60H05, 60H10, 60H20.

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