Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps
Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps
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DOI：
10.1016/j.spa.2007.06.009
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发表时间：
2008-05
影响因子：
1.4
通讯作者：
Jiaowan Luo;Kai Liu
中科院分区：
文献类型：
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作者：
Jiaowan Luo;Kai Liu
研究了Hilbert空间中由Lévy鞅驱动的马氏切换随机泛函微分方程的弱解的强解逼近方法.研究了Razumikhin-Lyapunov型函数方法和比较原理，得到了方程的矩指数稳定性和几乎处处指数稳定性的充分条件.结果[A. V. Svishchuk，Yu.I. Kazmerchuk，伊藤形式随机时滞方程的稳定性与跳跃和马尔可夫开关，及其在金融中的应用，Theor。可能吧数学统计学家64（2002）167-178]的结果，并将其作为我们理论的一个特例进行了推广和改进。
A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin–Lyapunov type function methods and comparison principles are studied in pursuit of sufficient conditions for the moment exponential stability and almost sure exponential stability of equations in which we are interested. The results of [A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance, Theor. Probab. Math. Statist. 64 (2002) 167–178] are generalized and improved as a special case of our theory.