Open Access
September 2013 Approximating dependent rare events
Louis H. Y. Chen, Adrian Röllin
Bernoulli 19(4): 1243-1267 (September 2013). DOI: 10.3150/12-BEJSP18


In this paper we give a historical account of the development of Poisson approximation using Stein’s method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on bootstrap percolation. We also discuss generalisations to compound Poisson approximation, Poisson process approximation and multivariate Poisson approximation, and state a few open problems.


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Louis H. Y. Chen. Adrian Röllin. "Approximating dependent rare events." Bernoulli 19 (4) 1243 - 1267, September 2013.


Published: September 2013
First available in Project Euclid: 27 August 2013

zbMATH: 1284.60110
MathSciNet: MR3102550
Digital Object Identifier: 10.3150/12-BEJSP18

Keywords: Bernoulli random variables , Bootstrap percolation , compound Poisson approximation , local dependence , maximal arithmetic progressions , monotone coupling , multivariate Poisson approximation , Poisson approximation , Poisson process approximation , Rare events , size-bias coupling , Stein’s method

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 4 • September 2013
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