Finite Dimensional Approximations of Hamilton-Jacobi-Bellman Equations in Probability Measure Spaces - SIAM PDE Seminar

Explore finite dimensional approximations of Hamilton-Jacobi-Bellman (HJB) equations in spaces of probability measures in this seminar presented by Andrzej Swiech from Georgia Tech. Delve into the convergence of viscosity solutions for HJB equations corresponding to deterministic and stochastic optimal control problems for particle systems. Examine the interpretation of the limiting HJB equation in its "lifted" form within a Hilbert space, and learn about the unique viscosity solution it possesses. Discover how, for first-order equations with convex Hamiltonians in the gradient variable, finite dimensional problem solutions converge to the value function of a variational problem in P2(R^d), providing a representation formula for the limiting HJB equation solution. Gain an overview of existing works and various approaches to partial differential equations in abstract spaces, including probability measure and Hilbert spaces. This seminar is based on joint work with W. Gangbo and S. Mayorga, offering valuable insights into advanced mathematical concepts in the field of partial differential equations.