STRONG APPROXIMATION RESULTS FOR THE EMPIRICAL PROCESS OF STATIONARY SEQUENCES

• 成果类型: Article
• 署名作者: Dedecker, Jerome; Merlevede, Florence; Rio, Emmanuel
• 署名单位: Universite Paris Cite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP798
• 发表日期: 2013
• 页码: 3658-3696
• 关键词: CENTRAL-LIMIT-THEOREM; INVARIANCE-PRINCIPLES; dependent sequences; unbounded functions; iterated logarithm; intermittent maps; random-variables; U-statistics; partial-sums; CONVERGENCE

摘要

We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n(-1-delta) for some positive delta. This shows that our conditions are in some sense optimal.