Bernoulli

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

Approximating dependent rare events

Louis H. Y. Chen and Adrian Röllin

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1377612850

Digital Object Identifier
doi:10.3150/12-BEJSP18

Mathematical Reviews number (MathSciNet)
MR3102550

Zentralblatt MATH identifier
1284.60110

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

Citation

Chen, Louis H. Y.; Röllin, Adrian. Approximating dependent rare events. Bernoulli 19 (2013), no. 4, 1243--1267. doi:10.3150/12-BEJSP18. https://projecteuclid.org/euclid.bj/1377612850


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