Abstract semilinear stochastic Itó-Volterra integrodifferential equations

David N. Keck and Mark A. McKibben

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-22

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 integrodifferential 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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:045253

DOI: 10.1155/JAMSA/2006/45253

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