The compound Poisson distribution and return times in dynamical systems

被引：45

作者：

Haydn, Nicolai ^{[1
]}

Vaienti, Sandro ^{[2
,3
,4
,5
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[2] CNRS, Ctr Phys Theor, UMR 6207, F-13288 Marseille 9, France

[3] Univ Aix Marseille 1, Federat Rech Unites Math Marseille, Marseille, France

[4] Univ Aix Marseille 2, Federat Rech Unites Math Marseille, Marseille, France

[5] Univ Toulon Var, Federat Rech Unites Math Marseille, Marseille, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 144卷 / 3-4期

关键词：

LIMIT LAWS; APPROXIMATION;

D O I：

10.1007/s00440-008-0153-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：

Previously it has been shown that some classes of mixing dynamical systems have limiting return times distributions that are almost everywhere Poissonian. Here we study the behaviour of return times at periodic points and show that the limiting distribution is a compound Poissonian distribution. We also derive error terms for the convergence to the limiting distribution. We also prove a very general theorem that can be used to establish compound Poisson distributions in many other settings.

引用

页码：517 / 542

页数：26

共 27 条

[1]

Abadi M., 2001, Markov Process. Relat. Fields, P97

[2] COMPOUND POISSON APPROXIMATION FOR NONNEGATIVE RANDOM-VARIABLES VIA STEIN METHOD [J].