崔静, 吴焕然. 带有脉冲和Poisson跳的随机积分微分方程渐近行为分析[J]. 应用概率统计, 2025, 41(6): 864-889. DOI: 10.12460/j.issn.1001-4268.aps.2025.2022049
引用本文: 崔静, 吴焕然. 带有脉冲和Poisson跳的随机积分微分方程渐近行为分析[J]. 应用概率统计, 2025, 41(6): 864-889. DOI: 10.12460/j.issn.1001-4268.aps.2025.2022049
CUI Jing, WU Huanran, . Asymptotic Behavior Analysis for Stochastic Integro-Differential Equations with Impulses and Poisson Jumps[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(6): 864-889.
Citation: CUI Jing, WU Huanran, . Asymptotic Behavior Analysis for Stochastic Integro-Differential Equations with Impulses and Poisson Jumps[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(6): 864-889.

带有脉冲和Poisson跳的随机积分微分方程渐近行为分析

Asymptotic Behavior Analysis for Stochastic Integro-Differential Equations with Impulses and Poisson Jumps

  • 摘要: 本文在实可分Hilbert空间中,研究了一类依分布无限延迟的脉冲中立型随机积分微分方程,使用Banach不动点定理证明了温和解的存在性和渐近稳定性, 进而研究了该随机系统的Hyers-Ulam稳定性. 最后举例说明了所得结果的有效性.

     

    Abstract: In this work, we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space. By using the Banach fixed point principle, some suffcient conditions are derived to ensure the asymptotic stability of mild solutions. Moreover, we investigate the Hyers-Ulam stability for such stochastic system. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained results.

     

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