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
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1186,
author = {N.U. Ahmed},
title = {A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and L\`evy process and controlled by L\`evy measure},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {36},
year = {2016},
pages = {181-206},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1186}
}
N.U. Ahmed. 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) pp. 181-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1186/
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