Giovanni Conforti: Gradient and Hessian estimates for Hamilton-Jacobi-Bellman equations via coupling by reflection and applications
Abstract: Coupling methods provide with a powerful toolbox for analysing the long time behaviour of Markov processes. In particular coupling by reflection allows to establish sharp exponential convergence results in Wasserstein distance for the Fokker-Planck equation without having to rely on pointwise assumptions on the confinement potential. The purpose of this talk is to illustrate the construction of a variant of coupling by reflection that applies to possibly mean-field controlled diffusion processes and yields uniform in time gradient (and Hessian) estimates for the solution of the corresponding Hamilton-Jacobi-Bellman equations. In turn, these estimates are shown to be key to prove various kind of exponential turnpike properties for the optimal processes and controls.
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