Small Variance Estimators for Rare Event Probabilities

Abstract

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events defined through large exceedances of the empirical mean of summands of a random walk, in the domain of large or moderate deviations. The approximation of conditional density of the trajectory of the random walk is handled on long runs. The length of those runs which is compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical Importance Sampling schemes. Detailed algorithms are proposed.