MIN-MAX REPRESENTATIONS OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS AND APPLICATIONS IN RARE-EVENT SIMULATION

In this paper a duality relation between the Mane potential and Mather's action functional is derived 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 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.

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