AIMS Mathematics, 2020, 5(6): 6169-6182. doi: 10.3934/math.2020396.

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

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

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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Keywords 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. AIMS Mathematics, 2020, 5(6): 6169-6182. doi: 10.3934/math.2020396

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