IMA Complex Systems Seminar
1:30, Thursday, January 22,
2004
Importance sampling, large deviations, and differential games
Division of Applied Mathematics
Brown University
Providence, RI 02912
(Joint work with Paul Dupuis.) Importance sampling is a variance reduction
technique for efficient estimation of rare-event probabilities by Monte
Carlo. In standard importance sampling
schemes, the system is simulated using an a priori fixed change of measure
suggested by a large deviation analysis.
In this work, we consider adaptive importance sampling schemes. By "adaptive", we mean that the
change of measure depends on the sample history. The existence of asymptotically optimal adaptive schemes is
demonstrated in great generality. The
implementation of the adaptive schemes is carried out with the help of a
limiting Isaacs equation. The idea of
subsolution is also exploited for constructing implementation-friendly adaptive
schemes.