The compound Poisson distribution and return times in dynamical systems

• 成果类型: Article
• 署名作者: Haydn, Nicolai; Vaienti, Sandro
• 署名单位: University of Southern California; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Aix-Marseille Universite; Universite de Toulon
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0153-y
• 发表日期: 2009
• 页码: 517-542
• 关键词: limit laws; approximation

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.