STEIN METHOD AND POINT PROCESS-APPROXIMATION

被引:71
作者
BARBOUR, AD [1 ]
BROWN, TC [1 ]
机构
[1] UNIV WESTERN AUSTRALIA, NEDLANDS, WA 6009, AUSTRALIA
基金
澳大利亚研究理事会;
关键词
POISSON APPROXIMATION; POINT PROCESS; STEIN-CHEN METHOD; COUPLING; PALM PROBABILITY; IMMIGRATION-DEATH PROCESS; HARD-CORE MODEL;
D O I
10.1016/0304-4149(92)90073-Y
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The Stein-Chen method for Poisson approximation is adapted into a form suitable for obtaining error estimates for the approximation of the whole distribution of a point process on a suitable topological space by that of a Poisson process. The adaptation involves consideration of an immigration-death process on the topological space, whose equilibrium distribution is that of the approximating Poisson process the Stein equation has a simple interpretation in terms of the generator of the immigration-death process. The error estimates for process approximation in total variation do not have the 'magic' Stein-Chen multiplying constants, which for univariate approximation tend to zero as the mean gets larger, but examples, including Bernoulli trials and the hard-core model on the torus, show that this is not possible. By choosing weaker metrics on the space of distributions of point processes, it is possible to reintroduce these constants. The proofs actually yield an improved estimate for one of the constants in the univariate case.
引用
收藏
页码:9 / 31
页数:23
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