On the LIL for self-normalized sums of IID random variables
type: Item
instance of: scholarly article
title: On the LIL for self-normalized sums of IID random variables
zbMATH Open document ID: 0919.60047
DOI: 10.1023/A:1022675620729
author: Evarist Giné
author: David M. Mason
published in: Journal of Theoretical Probability
publication date: 1999-08-31T00:00:00Z
review text: Let \(X\), \(X_i\), \(i\in N\), be i.i.d. real random variables, and set \(S_n= \sum^n_{i=1} X_i\), \(V^2_n= \sum^n_{i=1} X^2_i\). It is shown that \(\limsup_{n\to\infty}| S_n|/V_n \sqrt{\log\log n}< \infty\) a.s. whenever the sequence of self-normalized sums \(| S_n|/V_n\) is stochastically bounded, and that this lim sup is a.s. positive if, in addition, \(X\) is in the Feller class. A criterion for the sequence of self-normalized sums to be stochastically bounded is given.
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1208788
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: self-normalized sums
reviewed by: Oleg K. Zakusilo
MaRDI profile type: Publication
full work available at URL: a:1022675620729
OpenAlex ID: W1482583618
description: scientific article; zbMATH DE number 1208788