Branching and Interacting Particle Interpretations of Rare Event Probabilities

Abstract

This article focuses on branching particle interpretations of rare events. We connect importance sampling techniques with interacting particle algorithms, and multi-splitting branching models. These Monte Carlo methods are illustrated with a variety of examples arising in particle trapping analysis, as well as in ruin type estimation problems. We also provide a rather detailed presentation of the asymptotic theory of these particle algorithms, including exponential extinction probabilities, $\mathbb{L}_p$-mean error bounds, central limit theorem, and fluctuation variance comparaisons.