Annealed and quenched limit theorems for random expanding dynamical systems

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• 作者：Romain Aimino ; Matthew Nicol ; Sandro Vaienti
• 关键词：Random dynamical systems ; Limit theorems ; Borel–Cantelli lemmas ; Erd?s–Rényi laws ; Concentration inequalities ; 37H99 ; 37A25 ; 37D20
• 刊名：Probability Theory and Related Fields
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：162
• 期：1-2
• 页码：233-274
• 全文大小：700 KB
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• 作者单位：Romain Aimino (1) (2)
  Matthew Nicol (3)
  Sandro Vaienti (1) (2)
  
  1. Aix Marseille Université, CNRS, CPT, UMR 7332, 13288?, Marseille, France
  2. Université de Toulon, CNRS, CPT, UMR 7332, 83957?, La Garde, France
  3. Department of Mathematics, University of Houston, Houston, TX, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Probability Theory and Stochastic Processes
  Mathematical and Computational Physics
  Quantitative Finance
  Mathematical Biology
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-2064

文摘

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure invariance principle. We also discuss the quenched central limit theorem, dynamical Borel–Cantelli lemmas, Erd?s–Rényi laws and concentration inequalities.