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.
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Del Moral, P., Lezaud, P. Branching and Interacting Particle Interpretations of Rare Event Probabilities. In: Blom, H.A.P., Lygeros, J. (eds) Stochastic Hybrid Systems. Lecture Notes in Control and Information Science, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11587392_9
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DOI: https://doi.org/10.1007/11587392_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33466-8
Online ISBN: 978-3-540-33467-5
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