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A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

Author

Listed:
  • Qi Wang

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • Huabin Chen

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • Chenggui Yuan

    (Department of Mathematics, Bay Campus, Swansea University, Swansea SA1 8EN, UK)

Abstract

This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:866-:d:767174
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    References listed on IDEAS

    as
    1. 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).
    2. Mao, Xuerong, 1996. "Razumikhin-type theorems on exponential stability of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 233-250, December.
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    Cited by:

    1. Zihan Zou & Yinfang Song & Chi Zhao, 2022. "Razumikhin Theorems on Polynomial Stability of Neutral Stochastic Pantograph Differential Equations with Markovian Switching," Mathematics, MDPI, vol. 10(17), pages 1-15, August.

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