Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps

By Jiaowan Luo, Kai Liu. 2008

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A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Levy 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 Ito 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.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/36b4ccbce6a86df7ee9f09f699c17a6310da4b83