Small Deviation Probability via Chaining
Probability
2008-11-14 v2
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.
Cite
@article{arxiv.0706.2720,
title = {Small Deviation Probability via Chaining},
author = {Frank Aurzada and Mikhail Lifshits},
journal= {arXiv preprint arXiv:0706.2720},
year = {2008}
}