A generalized central limit theorem in infinite ergodic theory

• 成果类型: Article
• 署名作者: Thomine, Damien
• 署名单位: Universite de Rennes
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0491-2
• 发表日期: 2014
• 页码: 597-636
• 关键词: dynamical-systems; LAWS

摘要

We prove a generalized central limit theorem for dynamical systems with an infinite ergodic measure which induce a Gibbs-Markov map on some subset, provided the return time to this subset has regularly varying tails. We adapt a method designed by Csaki and Foldes for observables of random walks to show that the partial sums of some functions of the system-the return time and the observable-are asymptotically independent. Some applications to random walks and Pomeau-Manneville maps are discussed.