# 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 (2016)

- Volume: 36, Issue: 2, page 181-206
- ISSN: 1509-9407

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topN.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 36.2 (2016): 181-206. <http://eudml.org/doc/289593>.

@article{N2016,

abstract = {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},

author = {N.U. Ahmed},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {McKean-Vlasov stochastic differential equation; Hilbert spaces; existence of optimal controls},

language = {eng},

number = {2},

pages = {181-206},

title = {A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure},

url = {http://eudml.org/doc/289593},

volume = {36},

year = {2016},

}

TY - JOUR

AU - N.U. Ahmed

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

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2016

VL - 36

IS - 2

SP - 181

EP - 206

AB - 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

LA - eng

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

UR - http://eudml.org/doc/289593

ER -

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