English

Approximating dependent rare events

Probability 2013-10-09 v3 Statistics Theory Statistics Theory

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.

Keywords

Cite

@article{arxiv.1306.4158,
  title  = {Approximating dependent rare events},
  author = {Louis H. Y. Chen and Adrian Röllin},
  journal= {arXiv preprint arXiv:1306.4158},
  year   = {2013}
}

Comments

Published in at http://dx.doi.org/10.3150/12-BEJSP18 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

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