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.
Journal of Applied Mathematics and Stochastic Analysis
Article ID 45253
Keck, D. N., & McKibben, M. A. (2006). Abstract semilinear Itó-Volterra integro-differential stochastic evolution equations. Journal of Applied Mathematics and Stochastic Analysis, Article ID 45253, 1-22. Retrieved from http://digitalcommons.wcupa.edu/math_facpub/6