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Full-Text Articles in Physical Sciences and Mathematics
On A Class Of Backward Mckean-Vlasov Stochastic Equations In Hilbert Space: Existence And Convergence Properties, Nazim I. Mahmudov, Mark A. Mckibben
On A Class Of Backward Mckean-Vlasov Stochastic Equations In Hilbert Space: Existence And Convergence Properties, Nazim I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
This investigation is devoted to the study of a class of abstract first-order backward McKean-Vlasov stochastic evolution equations in a Hilbert space. Results concerning the existence and uniqueness of solutions and the convergence of an approximating sequence of solutions (and corresponding probability measures) are established. Examples that illustrate the abstract theory are also provided.
On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben
On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
In this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in Hilbert spaces under non Lipschitz condition is established. The applicability of this result is then illustrated in a discussion of some concrete backward stochastic partial differential equation. Furthermore, stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in Hilbert spaces is obtained.