Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal initial condition. Two examples illustrating the applicability of the general theory are provided.
Far East Journal of Mathematical Sciences
Pushpa Publishing House
McKibben, M. A. (2016). General existence results for abstract McKean-Vlasov stochastic equations with variable delay. Far East Journal of Mathematical Sciences, 99(9), 1335-1370. Retrieved from https://digitalcommons.wcupa.edu/math_facpub/23