Small deviation probability via chaining

Frank Aurzada and Mikhail Lifshits

Stochastic Processes and their Applications, 2008, vol. 118, issue 12, 2344-2368

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.

Keywords: Small; deviation; Lower; tail; probability; Chaining; Metric; entropy; Gaussian; processes; Stable; processes (search for similar items in EconPapers)
Date: 2008
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