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September 2013 Strong approximation results for the empirical process of stationary sequences
Jérôme Dedecker, Florence Merlevède, Emmanuel Rio
Ann. Probab. 41(5): 3658-3696 (September 2013). DOI: 10.1214/12-AOP798

Abstract

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.

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Jérôme Dedecker. Florence Merlevède. Emmanuel Rio. "Strong approximation results for the empirical process of stationary sequences." Ann. Probab. 41 (5) 3658 - 3696, September 2013. https://doi.org/10.1214/12-AOP798

Information

Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1284.60069
MathSciNet: MR3127895
Digital Object Identifier: 10.1214/12-AOP798

Subjects:
Primary: 37E05 , 60F17 , 60G10

Keywords: intermittent maps , Kiefer process , Stationary sequences , strong approximation , Weak dependence

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 5 • September 2013
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