Document Type
Article
Publication Date
5-2016
Abstract
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.
Publication Title
Far East Journal of Mathematical Sciences
ISSN
0972-0871
Publisher
Pushpa Publishing House
Volume
99
Issue
9
First Page
1335
Last Page
1370
Recommended Citation
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