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Almost sure exponential stability of stochastic reaction diffusion systems. (English) Zbl 1238.60065
Summary: The Lyapunov direct method, as the most effective measure of studying stability theory for ordinary differential systems and stochastic ordinary differential systems, has not been generalized to research concerning stochastic partial differential systems owing to the emptiness of the corresponding Ito differential formula. The goal of this paper is just employing the Lyapunov direct method to investigate the stability of Ito stochastic reaction diffusion systems, including asymptotical stability in probability and almost sure exponential stability. The obtained results extend the conclusions of {\it X.X. Liao} and {\it X.R. Mao} [Stochastic Anal. Appl. 14, No. 2, 165--185 (1996; Zbl 0848.60058)] and {\it X.X. Liao} et al. [Sci. China, Ser. F 44, No. 5, 389--395 (2001; Zbl 1238.93071)].

60H10Stochastic ordinary differential equations
Full Text: DOI
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