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Article
Abstract semilinear Itó-Volterra integro-differential stochastic evolution equations
Journal of Applied Mathematics and Stochastic Analysis
Document Type
Article
Publication Date
11-1-2006
Disciplines
Abstract
We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodi fferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.
Citation Information
David N. Keck and Mark A. McKibben. "Abstract semilinear Itó-Volterra integro-differential stochastic evolution equations" Journal of Applied Mathematics and Stochastic Analysis Vol. Article ID 45253 (2006) p. 1 - 22 Available at: http://works.bepress.com/mark_mckibben/6/