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Zbl 0789.60051
Govindan, T.E.
Autonomous semilinear stochastic Volterra integro-differential equations in Hilbert spaces. (English)
[J] Dyn. Syst. Appl. 3, No.1, 51-74 (1994). ISSN 1056-2176

Summary: We shall study semilinear stochastic integro-differential equations in a Hilbert space. We first prove several existence and uniqueness theorems with the assumption of global and local Lipschitz conditions on the nonlinear terms via Banach's contraction mapping principle. We also consider many interesting approximation problems associated with such equations. Lastly, employing Itô's formula we establish exponential mean square stability of the mild solution of such systems.

MSC 2000:: *60H20 Stochastic integral equations
60H05 Stochastic integrals
93E15 Stochastic stability

Keywords: semilinear stochastic integro-differential equations; Hilbert space; contraction mapping principle; mean square stability; mild solution

Cited in: Zbl 0855.60058

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