Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156267 | Stochastic Processes and their Applications | 2008 | 25 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Frank Aurzada, Mikhail Lifshits,