Approximating dependent rare events

作者：Chen Louis H Y^*; Roellin Adrian

来源：Bernoulli, 2013, 19(4): 1243-1267.

DOI：10.3150/12-BEJSP18

• 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

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.

• 出版日期2013-9