Asymptotic Normality in Banach Spaces via Lindeberg Method

Alfredas Račkauskas () and Charles Suquet ()
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Alfredas Račkauskas: Vilnius University
Charles Suquet: Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé

Journal of Theoretical Probability, 2023, vol. 36, issue 1, 409-455

Abstract: Abstract 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.

Keywords: Lindeberg method; Smooth Banach space; Triangular array; 60B10; 60B12; 60F05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01177-x

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