The Annals of Probability

Majorization, Exponential Inequalities and Almost Sure Behavior of Vector-Valued Random Variables

Erich Berger

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Abstract

In this paper we describe a general device that allows us to deduce various kinds of theorems (moment estimates, exponential inequalities, strong law of large numbers, stability results, bounded law of the iterated logarithm) for partial sums of independent vector-valued random variables from related results for partial sums of independent real-valued random variables. The concept of majorization will play a key role in our considerations.

Article information

Source
Ann. Probab., Volume 19, Number 3 (1991), 1206-1226.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990341

Digital Object Identifier
doi:10.1214/aop/1176990341

Mathematical Reviews number (MathSciNet)
MR1112413

Zentralblatt MATH identifier
0757.60002

JSTOR
links.jstor.org

Subjects
Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60F10: Large deviations 60F15: Strong theorems 60E15: Inequalities; stochastic orderings 60G50: Sums of independent random variables; random walks

Keywords
Majorization moment inequalities exponential inequalities strong law of large numbers bounded law of the iterated logarithm

Citation

Berger, Erich. Majorization, Exponential Inequalities and Almost Sure Behavior of Vector-Valued Random Variables. Ann. Probab. 19 (1991), no. 3, 1206--1226. doi:10.1214/aop/1176990341. https://projecteuclid.org/euclid.aop/1176990341


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