The Annals of Probability

Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes

M. Ledoux and M. Talagrand

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Abstract

In this paper, we obtain several new results and developments in the study of empirical processes. A comparison theorem for Rademacher averages is at the basis of the first part of the results, with applications, in particular, to Kolmogorov's law of the iterated logarithm and Prokhorov's law of large numbers for empirical processes. We then study the behavior of empirical processes along a class of functions through random geometric conditions and complete in this way the characterization of the law of the iterated logarithm. Bracketing and local Lipschitz conditions provide illustrations of some of these ideas to concrete situations.

Article information

Source
Ann. Probab., Volume 17, Number 2 (1989), 596-631.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991418

Digital Object Identifier
doi:10.1214/aop/1176991418

Mathematical Reviews number (MathSciNet)
MR985381

Zentralblatt MATH identifier
0679.60048

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case) 60F05: Central limit and other weak theorems

Keywords
Empirical processes comparison theorems random geometry limit theorems

Citation

Ledoux, M.; Talagrand, M. Comparison Theorems, Random Geometry and Some Limit Theorems for Empirical Processes. Ann. Probab. 17 (1989), no. 2, 596--631. doi:10.1214/aop/1176991418. https://projecteuclid.org/euclid.aop/1176991418


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