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Zbl 1165.60024
Luo, Jiaowan
Exponential stability for stochastic neutral partial functional differential equations. (English)
[J] J. Math. Anal. Appl. 355, No. 1, 414-425 (2009). ISSN 0022-247X

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 {\it T. E. Govindan} [Stochastics 77, 139--154 (2005; Zbl 1115.60064)], {\it K. Liu} and {\it A. Truman} [Statist. Probab. Lett. 50, 273--278 (2000; 0966.60059)] and {\it T. Taniguchi} [Stoch. Anal. Appl. 16, 965--975 (1998; 0911.60054); Stochastics 53, 41--52 (1995; Zbl 0854.60051)] are generalized and improved.

MSC 2000:: *60H15 Stochastic partial differential equations
93E15 Stochastic stability

Keywords: stochastic neutral partial functional differential equations; mild solutions; exponential stability in mean square and almost sure sense

Citations: Zbl 1115.60064; Zbl 0854.60051

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