Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps |
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Authors: | Jiaowan Luo Kai Liu |
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Institution: | 1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510405, PR China;2. Division of Statistics and Probability, Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool, L69 7ZL, United Kingdom |
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Abstract: | 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. |
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Keywords: | primary 93E03 secondary 60H10 |
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