Open Access
Translator Disclaimer
April, 1973 Maximal Inequalities and the Law of the Iterated Logarithm
William F. Stout
Ann. Probab. 1(2): 322-328 (April, 1973). DOI: 10.1214/aop/1176996985

Abstract

A supermartingale maximal inequality is derived. A maximal inequality is derived for arbitrary random variables $\{S_n, n \geqq 1\}$ (let $S_0 = 0$) satisfying $E\exp\lbrack u(S_{m + n} - S_m) \rbrack \leqq \exp(Knu^2)$ for all real $u$, all integers $m \geqq 0$ and $n \geqq 1$, and some constant $K$. These two maximal inequalities are used to derive upper half laws of the iterated logarithm for supermartingales, multiplicative random variables, and random variables not satisfying particular dependence assumptions.

Citation

Download Citation

William F. Stout. "Maximal Inequalities and the Law of the Iterated Logarithm." Ann. Probab. 1 (2) 322 - 328, April, 1973. https://doi.org/10.1214/aop/1176996985

Information

Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0262.60016
MathSciNet: MR353428
Digital Object Identifier: 10.1214/aop/1176996985

Subjects:
Primary: 60F15
Secondary: 60G40 , 60G45 , 60G99

Keywords: equinormed strongly multiplicative random variables , generalized Gaussian random variables , Law of the iterated logarithm , martingale , maximal inequality , multiplicative random variables , supermartingale

Rights: Copyright © 1973 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.1 • No. 2 • April, 1973
Back to Top