Geodesic
A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 181-206.

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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
Keywords: McKean-Vlasov stochastic differential equation, Hilbert spaces, existence of optimal controls 
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Ahmed, N. A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 36 (2016) no. 2, pp. 181-206. http://geodesic.mathdoc.fr/item/DMDICO_2016_36_2_a3/

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