Tail bounds via generic chaining

Sjoerd Dirksen

Tail bounds via generic chaining

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arxiv 1309.3522 v2 pith:2ZRO5A7A submitted 2013-09-13 math.PR cs.ITmath.IT

Sjoerd Dirksen This is my paper · ORCID

classification math.PRcs.ITmath.IT

keywords boundschainingdeviationgenericprocessessupremumtailupper

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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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