Boundedness analysis of non-autonomous stochastic differential systems with Lévy noise and mixed delays

Danhua He; Liguang Xu; Danhua He; Liguang Xu

doi:10.3934/math.2020396

AIMS Mathematics

2020, Volume 5, Issue 6: 6169-6182. doi: 10.3934/math.2020396

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Research article

Boundedness analysis of non-autonomous stochastic differential systems with Lévy noise and mixed delays

Danhua He ¹,
Liguang Xu ^{2
,
,}

1.
Department of Mathematics, Zhejiang International Studies University, Hangzhou 310023, PR China
2.
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, PR China

Received: 26 June 2020 Accepted: 28 July 2020 Published: 31 July 2020
MSC : 34K50, 34K20, 60G51

The present research studies the boundedness issue of Lévy driven non-autonomous stochastic differential systems with mixed discrete and distributed delays. A set of sufficient conditions of the $p$th moment globally asymptotical boundedness is obtained by combining the Lyapunov function method with the inequality technique. The proposed results reveal that the convergence rate $\lambda$ and the coefficients of the estimates for Lyapunov function $W$ and Itô operator $\mathcal {L}W$ can determine the upper bound for the solution. The presented results are demonstrated by an illustrative example.
- stochastic differential systems,
- Lévy noise, mixed delays,
- asymptotical boundedness
Citation: Danhua He, Liguang Xu. Boundedness analysis of non-autonomous stochastic differential systems with Lévy noise and mixed delays[J]. AIMS Mathematics, 2020, 5(6): 6169-6182. doi: 10.3934/math.2020396

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Abstract

The present research studies the boundedness issue of Lévy driven non-autonomous stochastic differential systems with mixed discrete and distributed delays. A set of sufficient conditions of the $p$th moment globally asymptotical boundedness is obtained by combining the Lyapunov function method with the inequality technique. The proposed results reveal that the convergence rate $\lambda$ and the coefficients of the estimates for Lyapunov function $W$ and Itô operator $\mathcal {L}W$ can determine the upper bound for the solution. The presented results are demonstrated by an illustrative example.

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