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arXiv · 1406.3605

Min-max representations of viscosity solutions of Hamilton-Jacobi equations and applications in rare-event simulation

Boualem Djehiche·Henrik Hult·Pierre Nyquist
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Abstract

In this paper a duality relation between the Ma\~{n}\'e 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 class\-es 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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Boualem Djehiche, Henrik Hult, Pierre Nyquist. 2014-06-13. Min-max representations of viscosity solutions of Hamilton-Jacobi equations and applications in rare-event simulation. https://arxiv.org/abs/1406.3605

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