Central limit theorem for the Walsh system
type: Item
instance of: scholarly article
title: Central limit theorem for the Walsh system
zbMATH Open document ID: 0587.60024
DOI: 10.1007/BF01141947
author: S. V. Levizov
published in: Mathematical Notes
publication date: 1984-01-01T00:00:00Z
review text: It is well-known that a lacunary orthogonal system of functions bears similar properties to the independent random variables. This paper investigates a problem which remained open in a paper of the reviewer, Stud. Sci. Math. Hung. 10(1975), 141-146 (1977; Zbl 0365.60031), concerning the validity of the central limit theorem in case of strongly lacunary Walsh systems. The author proves that under the lacunarity condition \[ n_{k+1}/n_ k\geq 1+c/\sqrt{k}\quad (c>0,\quad \alpha =1/2) \] there exists a sequence \(\{n_ k\}\) satisfying the above condition such that for the subsystem \(\{W_{n_ k}(x)\}\) of the Walsh functions the central limit theorem is not valid.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3942609
zbMATH Keywords: lacunary orthogonal system of functions
zbMATH Keywords: central limit theorem
zbMATH Keywords: strongly lacunary Walsh systems
zbMATH Keywords: Walsh functions
reviewed by: Antónia Földes
MaRDI profile type: Publication
cites work: On Lacunary trigonometric series, II
description: scientific article; zbMATH DE number 3942609