A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure

• Autorzy: N.U. Ahmed
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider McKean-Vlasov stochastic evolution equations on Hilbert spaces driven by Brownian motion and L`evy process and controlled by L`evy measures. We prove existence and uniqueness of solutions and regularity properties thereof. We consider weak topology on the space of bounded Le´vy measures on infinite dimensional Hilbert space and prove continuous dependence of solutions with respect to the Le´vy measure. Then considering a certain class of Le´vy 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

Słowa kluczowe

EN

McKean-Vlasov stochastic differential equation; Hilbert spaces; existence of optimal controls

Kategorie tematyczne

• 93E20: Optimal stochastic control
• 49J27: Problems in abstract spaces
• 60H15: Stochastic partial differential equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2016
• Tom: 36
• Numer: 2
• Strony: 181-206

Daty

wydano

2016

otrzymano

2016-11-30

Twórcy

autor

N.U. Ahmed

• University of Ottawa, Canada

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico.1186