ALMOST SURE INVARIANCE PRINCIPLE FOR DYNAMICAL SYSTEMS BY SPECTRAL METHODS

• 成果类型: Article
• 署名作者: Gouezel, Sebastien
• 署名单位: Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP525
• 发表日期: 2010
• 页码: 1639-1671
• 关键词: CENTRAL LIMIT-THEOREMS; MAPS; diffeomorphisms; approximation; EXTENSIONS; FLOWS

摘要

We prove the almost sure invariance principle for stationary R(d)-valued random processes (with very precise dimension-independent error terms). solely under a strong assumption concerning the characteristic functions of these processes This assumption is easy to check for large classes of dynamical systems or Markov chains using strong or weak spectral perturbation arguments