A universal form of the Chung-type law of the iterated logarithm
type: Item
instance of: scholarly article
title: A universal form of the Chung-type law of the iterated logarithm
zbMATH Open document ID: 0903.60053
author: Harry Kesten
published in: The Annals of Probability
publication date: 1999-01-05T00:00:00Z
review text: Consider an i.i.d. sequence \(X_1,X_2,\dots\) of real-valued random variables, and let \(S_n= X_1+\cdots+ X_n\) \((n= 1,2,\dots)\). A universal Chung-type law of the iterated logarithm is proved, that is, necessary and sufficient conditions for the existence of sequences \((a_n)\) and \((b_n)\) are found (under some side conditions) such that \(0<\liminf_{n\to\infty} b^{-1}_n \max_{j= 1,\dots,n} | S_j- a_j|< \infty\) w.p. 1.
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1130479
zbMATH Keywords: partial sums
reviewed by: J. G. Steinebach
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1023481104
OpenAlex ID: W2086578635
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DOI: 10.1214/AOP/1023481104
description: scientific article; zbMATH DE number 1130479