Limit law and rate of clustering for geometrically weighted random series
type: Item
instance of: scholarly article
title: Limit law and rate of clustering for geometrically weighted random series
zbMATH Open document ID: 1037.60030
DOI: 10.1016/S1631-073X(03)00016-5
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2003-01-01T00:00:00Z
review text: The author studies the behaviour of sums of the form \(S(\beta)=\sum_{n=0}^\infty\beta^nX_n\), where \(X_n\) are independent real random variables and \(\beta<1\) is a real number. It is known that if \(X_i\) are centered, i.i.d. random variables that have finite second moments, upon proper rescaling with a function of \(\beta\), \(S(\beta)\) satisfies a central limit theorem and a law of the iterated logarithm [the reviewer and \textit{P. Picco}, Ann. Probab. 21, 168--184 (1993; Zbl 0770.60029)]. It is also known that the same holds true if \(X_n\) are Gaussian and their variances satisfy a Kolmogorov-type condition [\textit{L.-X. Zhang}, ibid. 25, 1621--1635 (1997; Zbl 0903.60017)]. The author proves a functional form of these limit theorems and gives estimates on the speed of convergence.
reviewed by: Anton Bovier
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1907792
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: geometrically weighted sums
zbMATH Keywords: functional law of the iterated logarithm
author: George Stoica
MaRDI profile type: Publication
cites work: Q4387134
cites work: On the law of the iterated logarithm for canonical \(U\)-statistics and processes
cites work: A law of the iterated logarithm for random geometric series
cites work: Q4387142
cites work: Moderate deviations of dependent random variables related to CLT
cites work: Strong approximation theorems for geometrically weighted random series and their applications
description: scientific article; zbMATH DE number 1907792