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
Related Articles
- EP ID EP479225
- DOI 10.7151/dmdico.1186
- Views 43
- Downloads 0
On Schur-Cohn Stability of a Product of Operators in a Hilbert Space
A linear operator is said to be a Schur-Cohn stable one if its spectral radius is less than one. We consider the following problem: let A and B be bounded linear operators in a Hilbert space, and A be Schur-Cohn stable....
Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting
In this paper we consider an elastic thin film ωϵR2 with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-con...
Multiple Solutions for Dirichlet Impulsive Fractional Differential Inclusions Involving the p-Laplacian with Two Parameters
In this paper, the authors establish the existence of at least three weak solutions for impulsive differential inclusions involving two parameters and the p-Laplacian and having Dirichlet boundary conditions. Their appro...
A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure
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 regu...
Mild solutions for some partial functional integrodifferential equations with state-dependent delay
In this work, we establish sufficient conditions for the existence of solutions for some partial functional integrodifferential equations with state-dependent delay. We suppose that the undelayed part admits a resolvent...