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Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps

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  • Li, Guangjie
  • Yang, Qigui

Abstract

Few results seems to be known about the stability of numerical methods for the hybrid neutral stochastic functional differential equations with jumps (also known as the neutral stochastic functional differential equations with Markovian switching and jumps (NSFDEwMJs)). This paper mainly investigates the exponential stability (both the almost sure and the mean-square exponential stability) of the θ-method for NSFDEwMJs. Precisely, it is first illustrated that the trivial solution of the NSFDEwMJ is almost surely and mean-square exponentially stable. It is then shown that the θ-method can preserve the same conclusions of the trivial solution. Numerical examples are demonstrated to illustrate the obtained results.

Suggested Citation

  • Li, Guangjie & Yang, Qigui, 2021. "Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jumps," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004161
    DOI: 10.1016/j.chaos.2021.111062
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    References listed on IDEAS

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    1. Zhou, Shaobo, 2015. "Exponential stability of numerical solution to neutral stochastic functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 441-461.
    2. Hu, Rong, 2020. "Almost sure exponential stability of the Milstein-type schemes for stochastic delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Mo, Haoyi & Deng, Feiqi & Zhang, Chaolong, 2017. "Exponential stability of the split-step θ-method for neutral stochastic delay differential equations with jumps," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 85-95.
    4. Haoyi Mo & Xueyan Zhao & Feiqi Deng, 2017. "Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 462-470, February.
    5. Cui, Jing & Yan, Litan & Sun, Xichao, 2011. "Exponential stability for neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1970-1977.
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    Cited by:

    1. Qi Wang & Huabin Chen & Chenggui Yuan, 2022. "A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    2. Xiao, Hanni & Zhu, Quanxin & Karimi, Hamid Reza, 2022. "Stability analysis of semi-Markov switching stochastic mode-dependent delay systems with unstable subsystems," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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