Hitting and return times in ergodic dynamical systems

• 成果类型: Article
• 署名作者: Haydn, N; Lacroix, Y; Vaienti, S
• 署名单位: University of Southern California; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000242
• 发表日期: 2005
• 页码: 2043-2050
• 关键词: entrance times; limit laws; statistics; homeomorphisms

摘要

Given an ergodic dynamical system (X, T, mu), and U subset of X measurable with mu(U) > 0, let mu(U)tau(U)(x) denote the normalized hitting time of x is an element of X to U. We prove that given a sequence (U-n) with mu(U-n) -> 0, the distribution function of the normalized hitting times to U-n converges weakly to some subprobability distribution F if and only if the distribution function of the normalized return time converges weakly to some distribution function and that in the converging case, [GRAPHICS] This in particular characterizes asymptotics for hitting times, and shows that the asymptotics for return times is exponential if and only if the one for hitting times is also.