Abstract semilinear stochastic Itó-Volterraintegrodifferential equations

[摘要] We consider a class of abstract semilinear stochastic Volterraintegrodifferential equations in a real separable Hilbert space.The global existence and uniqueness of a mild solution, as well asa perturbation result, are established under the so-calledCaratheodory growth conditions on the nonlinearities. Anapproximation result is then established, followed by an analogousresult concerning a so-called McKean-Vlasov integrodifferentialequation, and then a brief commentary on the extension of the mainresults to the time-dependent case. The paper ends with adiscussion of some concrete examples to illustrate the abstracttheory.

[学科分类] 应用数学