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Boundedness analysis of stochastic delay differential equations with Lévy noise

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  • He, Danhua
  • Xu, Liguang

Abstract

The present paper is concerned with the mean square asymptotic boundedness and twice power almost surely asymptotic boundedness of stochastic delay differential equations driven by Lévy noise. First, mean square asymptotic boundedness criteria of the solutions are established by the method of reduction and the generalized Itô formula. Then, based on the Chebyshev inequality and the Borel–Cantelli lemma, the twice power almost surely asymptotic boundedness criteria are also derived for the addressed equations. Finally, a example is provided to demonstrate the validity of the proposed results.

Suggested Citation

  • He, Danhua & Xu, Liguang, 2022. "Boundedness analysis of stochastic delay differential equations with Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300321009851
    DOI: 10.1016/j.amc.2021.126902
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    References listed on IDEAS

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    1. Xu, Liguang & Dai, Zhenlei & Hu, Hongxiao, 2019. "Almost sure and moment asymptotic boundedness of stochastic delay differential systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 157-168.
    2. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    3. Zhao, Hongyong & Ding, Nan & Chen, Ling, 2009. "Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1653-1659.
    4. Wei Hu, 2018. "A New Stability Criterion for Neutral Stochastic Delay Differential Equations with Markovian Switching," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, October.
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