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Existence, Uniqueness and Stability Analysis for Neutral Stochastic Functional Differential Equations with Jumps and Infinite Delay

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  • Zuozheng Zhang

    (Beijing Institute of Technology)

  • Fubao Xi

    (Beijing Institute of Technology)

Abstract

This work focuses on a class of neutral stochastic functional differential equations with jumps and infinite delay (NSFDEwJI). First, we prove the existence and uniqueness of solution maps to NSFDEwJI using successive construction methods, and provide the exponential estimation of solution maps. Next, we establish the boundedness in pth moment of solution maps by Lyapunov function. Finally, with the aid of the Razumikhin argument, we obtain the exponential stability in pth moment. Based on this, the almost sure exponential stability is derived under a specific condition.

Suggested Citation

  • Zuozheng Zhang & Fubao Xi, 2025. "Existence, Uniqueness and Stability Analysis for Neutral Stochastic Functional Differential Equations with Jumps and Infinite Delay," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-35, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01396-4
    DOI: 10.1007/s10959-024-01396-4
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
    2. Mao, Wei & Zhu, Quanxin & Mao, Xuerong, 2015. "Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 252-265.
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