Rare event simulation and splitting for discontinuous random variables
ESAIM: Probability and Statistics, Tome 19 (2015), pp. 794-811.

Multilevel Splitting methods, also called Sequential Monte−Carlo or Subset Simulation, are widely used methods for estimating extreme probabilities of the form P[S(𝐔)>q] where S is a deterministic real-valued function and 𝐔 can be a random finite- or infinite-dimensional vector. Very often, X:=S(𝐔) is supposed to be a continuous random variable and a lot of theoretical results on the statistical behaviour of the estimator are now derived with this hypothesis. However, as soon as some threshold effect appears in S and/or 𝐔 is discrete or mixed discrete/continuous this assumption does not hold any more and the estimator is not consistent. In this paper, we study the impact of discontinuities in the cdf of X and present three unbiased corrected estimators to handle them. These estimators do not require to know in advance if X is actually discontinuous or not and become all equal if X is continuous. Especially, one of them has the same statistical properties in any case. Efficiency is shown on a 2-D diffusive process as well as on the Boolean SATisfiability problem (SAT).

Reçu le :
DOI : 10.1051/ps/2015017
Classification : 65C05 65C60 62L12 62N02
Mots-clés : Rare event simulation, multilevel splitting, RESTART, sequential Monte Carlo, extreme event estimation, counting, Last Particle Algorithm
Walter, Clément 1, 2

1 CEA, DAM, DIF, 91297 Arpajon, France
2 Laboratoire de Probabilités et Modèles Aléatoires, Université Paris Diderot, 75205 Paris cedex 05, France
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Walter, Clément. Rare event simulation and splitting for discontinuous random variables. ESAIM: Probability and Statistics, Tome 19 (2015), pp. 794-811. doi : 10.1051/ps/2015017. http://archive.numdam.org/articles/10.1051/ps/2015017/

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