A functional central limit theorem for \(\rho\) -mixing sequences
type: Item
instance of: scholarly article
title: A functional central limit theorem for \(\rho\) -mixing sequences
zbMATH Open document ID: 0547.60030
DOI: 10.1016/0047-259X(84)90073-3
author: Norbert Herrndorf
published in: Journal of Multivariate Analysis
publication date: 1984-01-01T00:00:00Z
review text: In this note a functional central limit theorem for \(\rho\) -mixing sequences of \textit{I. A. Ibragimov} [Teor. Veroyatn. Primen. 20, 134-140 (1975; Zbl 0335.60023); English translation in Theory Probab. Appl. 20, 135-141 (1975)] is generalized to non-stationary sequences \((X_ n)_{n\in {\mathbb{N}}}\), satisfying some assumptions on the variances and the moment condition \(E| X_ n|^{2+b}=0(n^{b/2-\epsilon})\) for some \(b>0\), \(\epsilon >0\). The main step in the argument is the proof of a suitable estimate for \(E|\sum^{n}_{i=1}X_ i|^{2+b}\).
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 3872385
zbMATH Keywords: maximal correlation
zbMATH Keywords: functional central limit theorem
MaRDI profile type: Publication
cites work: Q5560061
cites work: Central limit theorems under weak dependence
cites work: The invariance principle for ϕ-mixing sequences
cites work: Some Limit Theorems for Stationary Processes
cites work: A Note on the Central Limit Theorems for Dependent Random Variables
cites work: Invariance principles for mixing sequences of random variables
description: scientific article; zbMATH DE number 3872385