Functional central limit theorem and Strassen's law of the iterated logarithms for weakly multiplicative systems
type: Item
instance of: scholarly article
title: Functional central limit theorem and Strassen's law of the iterated logarithms for weakly multiplicative systems
zbMATH Open document ID: 0724.60037
author: Katusi Fukuyama
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: A sequence of r.v.'s \(X_ 1,X_ 2,..\). is called a multiplicative system if E \(X_{i_ 1}X_{i_ 2}...X_{i_ k}=0\) \((i_ 1<i_ 2<...<i_ k\); \(k=1,2,...)\). The central limit theorem and the law of iterated logarithm for multiplicative systems were proved (under some further restrictions) by several authors. In the present paper the weak and strong invariance principles are proved for multiplicative systems. The conditions used by the author meet with the weakest conditions used earlier to prove the central limit theorem and the law of iterated logarithm.
reviewed by: Pál Révész
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 4194841
zbMATH Keywords: multiplicative system
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: weak and strong invariance principles
zbMATH Keywords: central limit theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519953
OpenAlex ID: W1567255491
DOI: 10.1215/KJM/1250519953
description: scientific article; zbMATH DE number 4194841