Electronic Journal of Probability

Tail bounds via generic chaining

Sjoerd Dirksen

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We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.

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Electron. J. Probab., Volume 20 (2015), paper no. 53, 29 pp.

Accepted: 20 May 2015
First available in Project Euclid: 4 June 2016

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Generic chaining deviation inequalities suprema of empirical processes restricted isometry property chaos processes

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Dirksen, Sjoerd. Tail bounds via generic chaining. Electron. J. Probab. 20 (2015), paper no. 53, 29 pp. doi:10.1214/EJP.v20-3760. https://projecteuclid.org/euclid.ejp/1465067159

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