  Improving Importance Sampling estimators for rare event probabilities
requires sharp approx- imations of the optimal density leading to a nearly
zero-variance estimator. This paper presents a new way to handle the estimation
of the probability of a rare event defined as a finite intersection of subset.
We provide a sharp approximation of the density of long runs of a random walk
condi- tioned by multiples constraints, each of them defined by an average of a
function of its summands as their number tends to infinity.
