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Zbl 1115.60064
Govindan, T.E.
Almost sure exponential stability for stochastic neutral partial functional differential equations.
(English)
[J] Stochastics 77, No. 2, 139-154 (2005). ISSN 1744-2508; ISSN 1744-2516/e

A study on a new type of stochastic neutral functional differential equations in a real separable Hilbert space is presented. Some results on the existence and uniqueness of a mild solution and exponential stability of the moments of a solution are given. Also almost sure asymptotic behaviour of the sample paths is investigated. The obtained results are generalization of those reported in [Stochastics Stochastics Rep. 53, No. 1--2, 41--52 (1995; Zbl 0854.60051); Stochastic Anal. Appl. 16, No. 5, 965--975 (1998; Zbl 0911.60054)] and in the paper [A note on almost sure exponential stability for stochastic partial functional differential equations", Stat. Probab. Lett. 50, 273--278 (2000; Zbl 0966.60059)] by {\it K. Liu} and {\it A. Truman}. An example that illustrates the theory is presented as well.
[Wiesław Kotarski (Sosnowiec)]
MSC 2000:
*60H20 Stochastic integral equations
34K50 Stochastic delay equations
35B35 Stability of solutions of PDE
35R60 PDE with randomness

Keywords: stochastic neutral differential equations; mild solutions; exponential stability in the quadratic mean sense; almost sure asymptotic behaviour of the sample paths

Citations: Zbl 0854.60051; Zbl 0911.60054; Zbl 0966.60059

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