%0 Journal Article %T Towards zero variance estimators for rare event probabilities %A Michel Broniatowski %A Virgile Caron %J Mathematics %D 2011 %I arXiv %X 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. %U http://arxiv.org/abs/1104.1464v3