Law of the iterated logarithm in the Strassen formulation and additive functions
type: Item
instance of: scholarly article
title: Law of the iterated logarithm in the Strassen formulation and additive functions
zbMATH Open document ID: 0628.60043
DOI: 10.1007/BF00971346
published in: Lithuanian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The author obtained a law of iterated logarithm of Strassen type for sums of independent random variables. The method of proof is different from the standard one in the sense that the author avoids the difficult computation of obtaining lower exponential bounds by using the central limit theorem. The results are extended to sums of additive arithmetic functions. Detailed results are too technical to be formulated here. The basic idea goes back to \textit{A. de Acosta}, Ann. Probab. 11, 270-276 (1983; Zbl 0512.60014), in his proof of the Hartman-Wintner law of the iterated logarithm for independent identically distributed random variables.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 4022273
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: central limit theorem
zbMATH Keywords: additive arithmetic functions
author: Eugenijus Manstavičius
MaRDI profile type: Publication
cites work: Strong convergence of additive arithmetical functions
cites work: Q4085018
cites work: A new proof of the Hartman-Wintner law of the iterated logarithm
cites work: On the law of the iterated logarithm
cites work: Some Theorems on the Strong Law of Large Numbers and Law of the Iterated Logarithm
full work available at URL: https://doi.org/10.1007/bf00971346
OpenAlex ID: W2083595278
description: scientific article; zbMATH DE number 4022273