Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 45253, 22 pages

Abstract semilinear stochastic Itó-Volterra integrodifferential equations

David N. Keck1 and Mark A. McKibben2

1Department of Mathematics, Ohio University, Athens 45701, OH, USA
2Department of Mathematics and Computer Science, Goucher College, Baltimore 21204, MD, USA

Received 31 October 2005; Revised 3 March 2006; Accepted 14 April 2006

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.


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.