Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 45253, 22 pages
doi:10.1155/JAMSA/2006/45253
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.