Henrik Hult: Mane's potential, Hamilton-Jacobi equations and rare-event simulation

Abstract: We establish a duality between the Mané potential and the action functional in the context of convex and state-dependent Hamiltonians. The duality relation is used to obtain min-max representations of viscosity solutions of first order evolutionary Hamilton-Jacobi equations. These min-max representations naturally suggest classes of subsolutions of Hamilton-Jacobi equations that arise in the theory of large deviations. The subsolutions, in turn, are good candidates for designing efficient rare-event simulation algorithms. This is joint work with Boualem Djehiche and Pierre Nyquist.