Exponential stability for stochastic neutral partial functional differential equations |
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Authors: | Jiaowan Luo |
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Institution: | Department of Probability and Statistics, School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, PR China |
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Abstract: | In this paper, we consider a class of stochastic neutral partial functional differential equations in a real separable Hilbert space. Some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained. The known results in Govindan T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139-154], Liu and Truman K. Liu, A. Truman, A note on almost sure exponential stability for stochastic partial functional differential equations, Statist. Probab. Lett. 50 (2000) 273-278] and Taniguchi T. Taniguchi, Almost sure exponential stability for stochastic partial functional differential equations, Stoch. Anal. Appl. 16 (1998) 965-975; T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics 53 (1995) 41-52] are generalized and improved. |
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Keywords: | Stochastic neutral partial functional differential equations Mild solutions Exponential stability in mean square and almost sure sense |
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