International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2006 / Article

Open Access

Volume 2006 |Article ID 045253 | https://doi.org/10.1155/JAMSA/2006/45253

David N. Keck, Mark A. McKibben, "Abstract semilinear stochastic Itó-Volterra integrodifferential equations", International Journal of Stochastic Analysis, vol. 2006, Article ID 045253, 22 pages, 2006. https://doi.org/10.1155/JAMSA/2006/45253

Abstract semilinear stochastic Itó-Volterra integrodifferential equations

Received31 Oct 2005
Revised03 Mar 2006
Accepted14 Apr 2006
Published04 Jul 2006

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.

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Copyright © 2006 David N. Keck and Mark A. McKibben. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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