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Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.
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Dates et versions

hal-04141769 , version 1 (03-07-2023)
hal-04141769 , version 2 (10-07-2024)

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Aurélie Bigot. Central limit theorem under the Dedecker-Rio condition in some Banach spaces. 2024. ⟨hal-04141769v2⟩
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