## Section: New Results

### Estimation of extreme quantiles and isoquantile curves

Participants : François Le Gland, Rudy Pastel.

This is a collaboration with Jérôme Morio, from ONERA Châtillon.

Many reliability or hedging problems reduce to quantile estimation, and increasing safety standards creates a need for extreme quantile estimation. Adaptive multilevel splitting methods are studied in this context, which significantly reduce the variance of the relative error. A multilevel definition of quantile is proposed, under the name of isoquantile curves and is compared with the classical definition in terms of circular error probables. Its main advantage is a better use of the angular distribution, as illustrated in an example regarding the impact location of a ballistic launcher.