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Existence, Uniqueness, and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations in Hilbert Spaces

✍ Scribed by Takeshi Taniguchi; Kai Liu; Aubrey Truman

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 160 KB
Volume: 181
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.2001.4073

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✦ Synopsis

In this paper we shall consider the existence, uniqueness, and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r > 0: dX(t)=[ -AX(t)+f(t, X t )] dt+g(t, X t ) dW(t), where we assume that -A is a closed, densely defined linear operator and the generator of a certain analytic semigroup. f: (-., +.) × C a Q H, g: (-., +.) × C a Q L 0 2 (K, H) are two locally Lipschitz continuous functions, where

Here, W(t) is a given K-valued Wiener process and both H and K are separable Hilbert spaces.

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