The Annals of Probability

Some universal results on the behavior of increments of partial sums

Uwe Einmahl and David M. Mason

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Abstract

We establish very general one-sided results on the lim sup behavior of increments of suitably normalized partial sums of i.i.d. random variables. Our main results apply to arbitrary nondegenerate positive random variables which need not have any finite moments. As a corollary we can show that such results also hold for not necessarily positive random variables whose negative parts have finite moment-generating functions.

Article information

Source
Ann. Probab., Volume 24, Number 3 (1996), 1388-1407.

Dates
First available in Project Euclid: 9 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1065725186

Digital Object Identifier
doi:10.1214/aop/1065725186

Mathematical Reviews number (MathSciNet)
MR1411499

Zentralblatt MATH identifier
0872.60022

Subjects
Primary: 60F15: Strong theorems
Secondary: 60E07: Infinitely divisible distributions; stable distributions

Keywords
Universal law of the iterated logarithm quantile transformation maximal inequalities increments of partial sums

Citation

Einmahl, Uwe; Mason, David M. Some universal results on the behavior of increments of partial sums. Ann. Probab. 24 (1996), no. 3, 1388--1407. doi:10.1214/aop/1065725186. https://projecteuclid.org/euclid.aop/1065725186


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