Generalized law of the iterated logarithm and its convergence rate

Chen Pingyan; Qi Yongcheng

doi:10.1080/07362990601051997

Generalized law of the iterated logarithm and its convergence rate

Chen Pingyan, Qi Yongcheng

Mathematics & Statistics

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4 Scopus citations

Abstract

This article considers the partial sums from a sequence of independent and identically distributed random variables. It is well-known that the Hartman-Wintner law of the iterated logarithm holds if and only if the second moment exists. This article studies the generalized law of the iterated logarithm for the partial sums when they are normalized by a sequence of constants that are regularly varying with index 1/2. As a result, two equivalent conditions for the law are obtained.

Original language	English (US)
Pages (from-to)	89-103
Number of pages	15
Journal	Stochastic Analysis and Applications
Volume	25
Issue number	1
DOIs	https://doi.org/10.1080/07362990601051997
State	Published - Jan 1 2007

Bibliographical note

Funding Information:
Received December 15, 2005; Accepted August 15, 2006 The authors thank the referee for a careful reading of the manuscript and helpful comments. Chen’s research was supported by the National Nature Science Foundation of China, and Qi’s research was partially supported by NSF grant DMS-0604176.

Keywords

Complete convergence
Independent random variables
Laws of the iterated logarithm
Sums

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N2 - This article considers the partial sums from a sequence of independent and identically distributed random variables. It is well-known that the Hartman-Wintner law of the iterated logarithm holds if and only if the second moment exists. This article studies the generalized law of the iterated logarithm for the partial sums when they are normalized by a sequence of constants that are regularly varying with index 1/2. As a result, two equivalent conditions for the law are obtained.

AB - This article considers the partial sums from a sequence of independent and identically distributed random variables. It is well-known that the Hartman-Wintner law of the iterated logarithm holds if and only if the second moment exists. This article studies the generalized law of the iterated logarithm for the partial sums when they are normalized by a sequence of constants that are regularly varying with index 1/2. As a result, two equivalent conditions for the law are obtained.

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KW - Sums

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Generalized law of the iterated logarithm and its convergence rate

Abstract

Bibliographical note

Keywords

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