École Nationale Supérieure de
Techniques Avancées

Abstract

We consider the estimation of the probability µ of a union of J rare events Hj defined by a random variable X. To do this, we compare the ALOE estimator and the directional estimator from the papers [AC18] and [AK18] published the same year and which use two different approaches. The ALOE estimator is retained because of its better efficiency and its ability to be generalized to a large number of distributions. The latter, in the paper [AC18], is indeed only implemented for Gaussian distributions and rare events whose boundary is defined by a line. We modify this estimator using an adaptive multilevel splitting method to generalise it to a larger number of distributions and for rare events whose boundaries are defined more generally by the equation h(x) = τ where h : R d → R is a general function that we assume we can evaluate at any point x ∈ R d.This new estimator is compared to direct estimation of µ using the multilevel splitting method through a theoretical study and two numerical examples