Asymptotic Normality in Banach Spaces via Lindeberg Method

Račkauskas, Alfredas; Suquet, Charles

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s10959-022-01177-x

Title :

Asymptotic Normality in Banach Spaces via Lindeberg Method

Author(s) :

Račkauskas, Alfredas [Auteur]
Suquet, Charles [Auteur correspondant]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Theoretical Probability

Pages :

409-455

Publisher :

Springer

Publication date :

2022

ISSN :

0894-9840

English keyword(s) :

Lindeberg method
smooth Banach space
triangular array

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

The relation between weak convergence of probabilities on a smooth Banach space and uniform convergence over a certain class of smooth functions is established. This leads to an extension of Lindeberg’s proof of the central ...
Show more >The relation between weak convergence of probabilities on a smooth Banach space and uniform convergence over a certain class of smooth functions is established. This leads to an extension of Lindeberg’s proof of the central limit theorem in a Banach space framework. As a result, asymptotic normality is proved for sums of Banach space random variables including triangular arrays and weighted linear processes.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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