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

Research output: Contribution to journal › Article › peer-review

3 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

Keywords

Complete convergence
Independent random variables
Laws of the iterated logarithm
Sums

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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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