A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2016, Vol 36, Issue 2
Abstract
In this paper we consider McKean-Vlasov stochastic evolution equations on Hilbert spaces driven by Brownian motion and Lèvy process and controlled by Lèvy measures. We prove existence and uniqueness of solutions and regularity properties thereof. We consider weak topology on the space of bounded Lèvy measures on infinite dimensional Hilbert space and prove continuous dependence of solutions with respect to the Lèvy measure. Then considering a certain class of Lèvy measures on infinite as well as finite dimensional Hilbert spaces, as relaxed controls, we prove existence of optimal controls for Bolza problem and some simple mass transport problems.
Authors and Affiliations
NasirUddin Ahmed
Keywords
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- EP ID EP479225
- DOI 10.7151/dmdico.1186
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