Min-max representations of viscosity solutions of Hamilton-Jacobi equations and applications in rare-event simulation
(English)Manuscript (preprint) (Other academic)
In this paper a duality relation between the Mañé 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.
Hamilton-Jacobi equations, viscosity solutions, Monte Carlo methods
Probability Theory and Statistics Mathematical Analysis
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-144419OAI: oai:DiVA.org:kth-144419DiVA: diva2:713461
QS 20142014-04-232014-04-232014-04-24Bibliographically approved