Moment bounds for dependent sequences in smooth Banach spaces

2014/04/02 by Jérôme Dedecker, Dedecker, Jérôme, Florence Merlevède +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #37E05 #60E15 #60G48 #Advanced Banach Space Theory #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1404.0563

openalex publication_date 2014/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a Marcinkiewicz-Zygmund type inequality for random variables taking values in a smooth Banach space. Next, we obtain some sharp concentration inequalities for the empirical measure of \T, T², ⋯, Tⁿ\, on a class of smooth functions, when T belongs to a class of nonuniformly expanding maps of the unit interval.

Citations

• Recurrence times and rates of mixing
• Weak convergence of the empirical process of intermittent maps in L2 under long-range dependence

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