带Markov切换Poisson跳的随机泛函微分 方程解的存在性和稳定性
Existence and Stability of Solutionsto Stochastic Functional Di erentialEquations with Markovian Switchingand Poisson Jumps
摘要: 本文研究了一类带Markov切换Poisson跳的随机泛函微分方程。运用Lyapunov函数方法和随机分析技巧，研究了该类方程全局解的存在唯一性以及平凡解的均方指数稳定性和几乎必然稳定性。
Abstract: This paper investigates a class of stochastic functional differential equations with Markovian switching and Poisson jumps. By means of the Lyapunov function method and stochastic analysis techniques, this study establishes the existence and uniqueness of the global solution to such equations, as well as the mean-square exponential stability and the almost sure stability of the trivial solution.
文章引用：李光洁. 带Markov切换Poisson跳的随机泛函微分 方程解的存在性和稳定性[J]. 理论数学, 2026, 16(8): 124-130. https://doi.org/10.12677/PM.2026.168186

参考文献

[1] Appleby, J.A.D. and Mao, X. (2005) Stochastic Stabilisation of Functional Differential Equations. Systems & Control Letters, 54, 1069-1081. [Google Scholar] [CrossRef] 
[2] Zong, X., Yin, G., Wang, L.Y., Li, T. and Zhang, J. (2018) Stability of Stochastic Functional Differential Systems Using Degenerate Lyapunov Functionals and Applications. Automatica, 91, 197-207.[CrossRef] 
[3] Mao, X. (1997) Stochastic Differential Equations and Application. Horwood Publication Ltd.
[4] Mohammed, S.E.A. (1986) Stochastic Functional Differential Equations. Longman.
[5] Zhao, X. and Deng, F. (2014) New Type of Stability Criteria for Stochastic Functional Differential Equations via Lyapunov Functions. SIAM Journal on Control and Optimization, 52, 2319-2347.[CrossRef] 
[6] Bao, J., Yin, G. and Yuan, C. (2016) Asymptotic Analysis for Functional Stochastic Differential Equations. Springer.
[7] Kadiev, R. and Ponosov, A. (2022) The W-Method in Stability Analysis of Stochastic Functional Differential Equations. Functional Differential Equations, 29, 167-181.[CrossRef] 
[8] Mariton, M. (1990) Jump Linear Systems in Automatic Control. Taylor & Francis.
[9] Hanson, F.B. (2007) Applied Stochastic Processes and Control for Jump-Diffusion. SIAM.
[10] Mo, H., Li, M., Deng, F. and Mao, X. (2018) Exponential Stability of the Euler-Maruyama Method for Neutral Stochastic Functional Differential Equations with Jumps. Science China Information Sciences, 61, Article No. 70214.[CrossRef] 
[11] Anderson, W.J. (1991) Continuous-Time Markov Chains. Springer.
[12] Mao, X. and Yuan, C. (2006) Stochastic Differential Equations with Markovian Switching. Imperial College Press.
[13] Swishchuk, A.V. and Kazmerchuk, Y.I. (2001) Stability of Stochastic Differential Delay It's Equations with Poisson Jumps and with Markovian Switchings: Application to Financial Models. Theory of Probability and Mathematical Statistics, 64, 141-151.
[14] Zhang, W., Ye, J. and Li, H. (2014) Stability with General Decay Rates of Stochastic Differential Delay Equations with Poisson Jumps and Markovian Switching. Statistics & Probability Letters, 92, 1-11.[CrossRef] 
[15] Zhu, Q. (2016) Razumikhin-Type Theorem for Stochastic Functional Differential Equations with Levy Noise and Markov Switching. International Journal of Control, 90, 1703-1712.[CrossRef] 

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