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arXiv · 0706.2720

Small Deviation Probability via Chaining

Frank Aurzada·Mikhail Lifshits
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Abstract

We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential behaviour of covering numbers. The corresponding results are also proved for non-Gaussian symmetric stable processes, both for the cases of critically small and critically large entropy. The results extensively use the classical chaining technique; at the same time they are meant to explore the limits of this method.

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Frank Aurzada, Mikhail Lifshits. 2007-11-23. Small Deviation Probability via Chaining. https://doi.org/10.1016/j.spa.2008.01.005

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