Tata Institute of Fundamental Research
Minmax Representation of Viscosity Solutions to Hamilton-Jacobi Equations and Applications in Rare-event Simulation
STCS Seminar
Speaker:
Henrik Hult (Royal Institute of Technology
Department of Mathematics
SE-100 44 Stockholm
Sweden)
Organiser:
Sandeep K Juneja
Date:
Wednesday, 11 Feb 2015, 14:30 to 15:30
Venue:
AG-80
(Scan to add to calendar)
Abstract:
Abstract: In this talk a duality relation between the Mane's 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. I will show some applications to financial risk management and reliability of power systems.
| Speaker: | Henrik Hult (Royal Institute of Technology Department of Mathematics SE-100 44 Stockholm Sweden) |
| Organiser: | Sandeep K Juneja |
| Date: | Wednesday, 11 Feb 2015, 14:30 to 15:30 |
| Venue: | AG-80 |
(Scan to add to calendar)
Abstract:
Abstract: In this talk a duality relation between the Mane's 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. I will show some applications to financial risk management and reliability of power systems.