Central limit theorem under the Dedecker-Rio condition in some Banach spaces

2023/07/04 by Aurélie Bigot, Bigot, Aurélie
Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2307.01564

openalex publication_date 2023/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables taking values in L^p(μ), with 2 ≤ p < ∞ and μ a σ-finite real measure. As an application we give a sufficient condition for empirical processes indexed by Sobolev balls to satisfy the central limit theorem, and discuss about the optimality of these conditions.

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