Small deviation probability via chaining

Frank Aurzada, Mikhail Lifshits

Research output

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)2344-2368
Number of pages25
JournalStochastic Processes and their Applications
Volume118
Issue number12
DOIs
Publication statusPublished - 1 Dec 2008

Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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