A law of the iterated logarithm for geometrically weighted martingale difference sequences
type: Item
instance of: scholarly article
title: A law of the iterated logarithm for geometrically weighted martingale difference sequences
zbMATH Open document ID: 0802.60029
DOI: 10.1007/BF02214275
published in: Journal of Theoretical Probability
publication date: 1994-05-09T00:00:00Z
review text: Let \(Y_ n\), \(n\geq 1\), be a stationary and ergodic martingale difference sequence with \(E(Y^ 2_ 0)=1\), and for \(\beta<1\) set \(\xi(\beta)= \sum_{n=0}^ \infty \beta^ n Y_ n\). It is shown that the random variables \(\xi(\beta)\), when suitably normalized, obey a law of the iterated logarithm and a central limit theorem as \(\beta \nearrow 1\).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 566139
zbMATH Keywords: stationary and ergodic martingale difference sequence
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: central limit theorem
author: Pierre Picco
author: Maria Eulalia Vares
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02214275
OpenAlex ID: W2059641206
description: scientific article; zbMATH DE number 566139