LaSalle’s invariance principle for delay differential equations driven by α-stable processes

doi:10.3969/j.issn.1000-5641.2023.04.002

Journal of East China Normal University(Natural Science) ›› 2023, Vol. 2023 ›› Issue (4): 11-23.doi: 10.3969/j.issn.1000-5641.2023.04.002

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LaSalle’s invariance principle for delay differential equations driven by α-stable processes

Zhenzhong ZHANG(), Xu CHEN, Jinying TONG

College of Science, Donghua University, Shanghai　201620, China

Received:2021-09-24 Online:2023-07-25 Published:2023-07-25

Abstract

Abstract:

LaSalle’s invariance principle is an important tool for studying the stability of stochastic systems. Considering the influence of time delay and pure-jump path on the stability of the system and using the convergence theorem for special semi-martingale, the LaSalle’s invariance principle for a class of stochastic delay differential equations driven by $\alpha$ -stable processes is established in this study. The sufficient conditions for the asymptotic stability of a class of delay equations are given by LaSalle’s invariance principle.

Key words: LaSalle’s invariance principle, special semi-martingale, asymptotic stability in probability, stability in probability

CLC Number:

O211.63

Zhenzhong ZHANG, Xu CHEN, Jinying TONG. LaSalle’s invariance principle for delay differential equations driven by α-stable processes[J]. Journal of East China Normal University(Natural Science), 2023, 2023(4): 11-23.

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LaSalle’s invariance principle for delay differential equations driven by α-stable processes

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