Multilevel branching and splitting algorithm for estimating rare event probabilities

We analyze the splitting algorithm performance in the estimation of rare event probabilities in a discrete multidimensional framework. For this we assume that each threshold is partitioned into disjoint subsets and the probability for a particle to reach the next threshold will depend on the startin...

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Vydáno v:Simulation modelling practice and theory Ročník 72; číslo March 2017; s. 150 - 167
Hlavní autoři: Lagnoux, Agnès, Lezaud, Pascal
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.03.2017
Elsevier
Témata:
Branching process
Conformal maps
First crossing time density
Mathematics
Monte Carlo
Probability
Rare event probability estimation
Simulation
Splitting
Variance reduction
Rare event probability estimation
Splitting
Branching process
First crossing time density
Monte Carlo
Simulation
Variance reduction
Conformal maps
splitting
first crossing time density
variance reduction
simulation
branching process
rare event probability estimation
conformal maps
ISSN:1569-190X, 1878-1462
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Popis
Shrnutí:We analyze the splitting algorithm performance in the estimation of rare event probabilities in a discrete multidimensional framework. For this we assume that each threshold is partitioned into disjoint subsets and the probability for a particle to reach the next threshold will depend on the starting subset. A straightforward estimator of the rare event probability is given by the proportion of simulated particles for which the rare event occurs. The variance of this estimator is the sum of two parts: with one part resuming the variability due to each threshold, and the second part resuming the variability due to the number of thresholds. This decomposition is analogous to that of the continuous case. The optimal algorithm is then derived by cancelling the first term leading to optimal thresholds. Then we compare this variance with that of the algorithm in which one of the threshold has been deleted. Finally, we investigate the sensitivity of the variance of the estimator with respect to a shape deformation of an optimal threshold. As an example, we consider a two-dimensional Ornstein–Uhlenbeck process with conformal maps for shape deformation.
ISSN:1569-190X
1878-1462
DOI:10.1016/j.simpat.2016.12.009