The Annals of Probability

Some Applications of Isoperimetric Methods to Strong Limit Theorems for Sums of Independent Random Variables

M. Ledoux and M. Talagrand

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Abstract

We develop several applications to almost sure limit theorems for sums of independent vector valued random variables of an isoperimetric inequality due to Talagrand. A general treatment of the classical laws of large numbers of Kolmogorov and Prokorov and laws of the iterated logarithm of Kolmogorov and Hartman and Wintner is described. New results as well as simpler new proofs of known ones illustrate the usefulness of isoperimetric methods in this context. We show further how this approach can be used in the study of limit theorems for trimmed sums of independent and identically distributed random variables.

Article information

Source
Ann. Probab., Volume 18, Number 2 (1990), 754-789.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990857

Digital Object Identifier
doi:10.1214/aop/1176990857

Mathematical Reviews number (MathSciNet)
MR1055432

Zentralblatt MATH identifier
0713.60005

JSTOR
links.jstor.org

Subjects
Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60F15: Strong theorems

Keywords
Isoperimetric inequality law of large numbers law of the iterated logarithm trimming

Citation

Ledoux, M.; Talagrand, M. Some Applications of Isoperimetric Methods to Strong Limit Theorems for Sums of Independent Random Variables. Ann. Probab. 18 (1990), no. 2, 754--789. doi:10.1214/aop/1176990857. https://projecteuclid.org/euclid.aop/1176990857


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