Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise

Yanqiang Chang; Huabin Chen

doi:10.3934/dcdsb.2021301

Article Contents

2022, Volume 27, Issue 10: 5935-5952. Doi: 10.3934/dcdsb.2021301

This issue Previous Article Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart Next Article Global dynamics of a Huanglongbing model with a periodic latent period

Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise

Yanqiang Chang and
Huabin Chen^,

Department of Mathematics, Nanchang University, Nanchang 330031, China

^* Corresponding author: Huabin Chen
^* Corresponding author: Huabin Chen

Received: May 31, 2021

Revised: September 30, 2021

Early access: December 2021

Published: October 2022

Huabin Chen is partially supported by the National Natural Science Foundation of China (62163027), the National Social Science Foundation of China (21BTJ028), and the Natural Science Foundation of Jiangxi Province of China (20171BCB23001)

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Abstract

In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L$ \acute{e} $vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in $ p $th($ p\geq2 $) for stochastic delay differential equations with Markovian switching driven by L$ \acute{e} $vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.

Keywords:

L$ \acute{e} $vy noises,
Markovian switching,
stochastic delay differential equations,
existence and uniqueness,
stability analysis.

Mathematics Subject Classification: 58F15, 58F17, 53C35.

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