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SUMMARY:Andrzej Swiech (Georgia Tech\, USA)
DTSTART:20210204T163000Z
DTEND:20210204T173000Z
DTSTAMP:20260423T040043Z
UID:SIAM-PDE/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SIAM-PDE/7/"
 >Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in
  spaces of probability measures. (Featured Article in SIAM Journal on Math
 ematical Analysis)</a>\nby Andrzej Swiech (Georgia Tech\, USA) as part of 
 Seminar In the Analysis and Methods of PDE (SIAM PDE)\n\n\nAbstract\nWe wi
 ll discuss how certain Hamilton-Jacobi-Bellman (HJB) equations in spaces o
 f probability measures can be approximated by finite dimensional equations
 . The most interesting cases are convergence of viscosity solutions of HJB
  equations corresponding either to deterministic optimal control problems 
 for systems of $n$ particles or to stochastic optimal control problems for
  systems of $n$ particles with a common noise\, to the viscosity solution 
 of a limiting HJB equation in the space of probability measures. The limit
 ing HJB equation is interpreted in its ``lifted" form in a Hilbert space\,
  which has a unique viscosity solution. When the Hamiltonian is convex in 
 the gradient variable and equations are of first order\, it can be proved 
 that the viscosity solutions of the finite dimensional problems converge t
 o the value function of a variational problem in $\\mathcal{P}_2(\\R^d)$ t
 hus providing a representation formula for the solution of the limiting fi
 rst order HJB equation. The talk will also contain an overview of existing
  works and various approaches to partial differential equations in abstrac
 t spaces\, including spaces of probability measures and Hilbert spaces. Th
 e talk is based on a joint work with W. Gangbo and S. Mayorga.\n\nFeatured
  Article Authors: W. Gangbo\, S. Mayorga\, A. Swiech\n
LOCATION:https://researchseminars.org/talk/SIAM-PDE/7/
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