Rare event simulation and splitting for discontinuous random variables
type: Item
instance of: scholarly article
title: Rare event simulation and splitting for discontinuous random variables
zbMATH Open document ID: 1416.65022
author: Clément Walter
publication date: 2016-02-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1507.00919
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 62N02
zbMATH DE Number: 6541407
zbMATH Keywords: rare event simulation
zbMATH Keywords: multilevel splitting
zbMATH Keywords: sequential Monte Carlo
zbMATH Keywords: extreme event estimation
zbMATH Keywords: counting
zbMATH Keywords: last particle algorithm
MaRDI profile type: Publication
OpenAlex ID: W2963507303
arXiv ID: 1507.00919
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DOI: 10.1051/PS/2015017
published in: European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
review text: The authors study the impact of discontinuities in the cdf of a random variable \(X\) by means of three unbiased and corrected estimators. The particularity of the constructed estimators is the fact that they did not require in advance the variable \(X\) to be actually discontinuous or not. Existing studies as declared from the authors did not require the continuity of the cdf of \(X\). This was one first motivation behind the developments in the present paper. The authors studied both the distribution of the number of iterations and the MVUE estimator in the case with strict inequality and the one with non-strict inequality. Efficiency of the theoretical results has been shown also on some numerical examples based on a 2-dimensional diffusive process as well as on the well-known Boolean satisfiability problem.
reviewed by: Anouar Ben Mabrouk
description: scientific article; zbMATH DE number 6541407