• Bernoulli
  • Volume 19, Number 4 (2013), 1243-1267.

Approximating dependent rare events

Louis H. Y. Chen and Adrian Röllin

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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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Bernoulli, Volume 19, Number 4 (2013), 1243-1267.

First available in Project Euclid: 27 August 2013

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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


Chen, Louis H. Y.; Röllin, Adrian. Approximating dependent rare events. Bernoulli 19 (2013), no. 4, 1243--1267. doi:10.3150/12-BEJSP18.

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