Optimal Control of General McKean-Vlasov Stochastic Evolution Equations on Hilbert Spaces and Necessary Conditions of Optimality
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2015, Vol 35, Issue 2
Abstract
In this paper we consider controlled McKean-Vlasov stochastic evolution equations on Hilbert spaces. We prove existence and uniqueness of solutions and regularity properties thereof. We use relaxed controls, adapted to a current of sub-sigma algebras generated by observable processes, and taking values from a Polish space. We introduce an appropriate topology based on weak star convergence. We prove continuous dependence of solutions on controls with respect to appropriate topologies. Theses results are then used to prove existence of optimal controls for Bolza problems. Then we develop the necessary conditions of optimality based on semi-martingale representation theory on Hilbert spaces. Next we show that the adjoint processes arising from the necessary conditions optimality can be constructed from the solution of certain BSDE.
Authors and Affiliations
NasirUddin Ahmed
Keywords
Related Articles
- EP ID EP469504
- DOI 10.7151/dmdico.1171
- Views 75
- Downloads 0
Preface
-
On properties of set-valued integrals driven by martingales and set-valued stochastic equations
In the paper we study properties of stochastic integrals of Aumann type driven by quadratic variation process and set-valued Itô integral with respect to martingale. Next, the existence, uniqueness and convergence proper...
Boundedness of set-valued stochastic integrals
The paper deals with integrable boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrable bounded. The problem of in...
Multivalued anisotropic problem with Neumann boundary condition involving diffuse Radon measure data and variable exponent
We study a nonlinear anisotropic elliptic problem with homogeneous Neumann boundary condition governed by a general anisotropic operator with variable exponents and diffuse Radon measure data that is the Radon measure wh...
Necessary conditions of optimality for a class of stochastic differential equations on UMD Banach spaces
In this paper we consider stochastic evolution equations on UMD-Banach spaces. In a recent paper we proved existence of optimal controls. Here in this paper we develop necessary conditions of optimality whereby one can...