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Exponential stability for stochastic neutral partial functional differential equations. (English) Zbl 1165.60024
Summary: 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 T. E. Govindan [Stochastics 77, 139–154 (2005; Zbl 1115.60064)], K. Liu and A. Truman [Statist. Probab. Lett. 50, 273–278 (2000; Zbl 0966.60059)] and T. Taniguchi [Stoch. Anal. Appl. 16, 965–975 (1998; Zbl 0911.60054); Stochastics 53, 41–52 (1995; Zbl 0854.60051)] are generalized and improved.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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