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

Aurélie Bigot

Stochastic Processes and their Applications, 2024, vol. 176, issue C

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 Lp(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.

Date: 2024
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DOI: 10.1016/j.spa.2024.104419

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