Towards zero variance estimators for rare event probabilities
Probability
2012-02-08 v3
Abstract
Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a large or moderate deviation event. The approximation of the conditional density of the real r.v's X_{i} 's, for 1\leqi\leqk_{n} with repect to E_{n} on long runs, when k_{n}/n\to1, is handled. The maximal value of k compatible with a given accuracy is discussed; algorithms and simulated results are presented.
Cite
@article{arxiv.1104.1464,
title = {Towards zero variance estimators for rare event probabilities},
author = {Michel Broniatowski and Virgile Caron},
journal= {arXiv preprint arXiv:1104.1464},
year = {2012}
}