The Annals of Probability

Majorizing measures: the generic chaining

Michel Talagrand

Full-text: Open access

Abstract

Majorizing measures provide bounds for the supremum of stochastic processes. They represent the most general possible form of the chaining argument going back to Kolmogorov. Majorizing measures arose from the theory of Gaussian processes, but they now have applications far beyond this setting. The fundamental question is the construction of these measures. This paper focuses on the tools that have been developed for this purpose and, in particular, the use of geometric ideas. Applications are given to several natural problems where entropy methods are powerless.

Article information

Source
Ann. Probab. Volume 24, Number 3 (1996), 1049-1103.

Dates
First available in Project Euclid: 9 October 2003

Permanent link to this document
http://projecteuclid.org/euclid.aop/1065725175

Digital Object Identifier
doi:10.1214/aop/1065725175

Mathematical Reviews number (MathSciNet)
MR1411488

Zentralblatt MATH identifier
0867.60017

Subjects
Primary: 60G05: Foundations of stochastic processes 60G15: Gaussian processes
Secondary: 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]

Keywords
Chaining increment condition boundedness of trajectories Gaussian properties majorization measure matchings random restrictions of operators

Citation

Talagrand, Michel. Majorizing measures: the generic chaining. Ann. Probab. 24 (1996), no. 3, 1049--1103. doi:10.1214/aop/1065725175. http://projecteuclid.org/euclid.aop/1065725175.


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