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Small deviation probability via chaining

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  • Aurzada, Frank
  • Lifshits, Mikhail

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.

Suggested Citation

  • Aurzada, Frank & Lifshits, Mikhail, 2008. "Small deviation probability via chaining," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2344-2368, December.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:12:p:2344-2368
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    References listed on IDEAS

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    1. Linde, Werner & Shi, Zhan, 2004. "Evaluating the small deviation probabilities for subordinated Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 273-287, October.
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    Cited by:

    1. Oliver Kley, 2013. "Kuelbs–Li Inequalities and Metric Entropy of Convex Hulls," Journal of Theoretical Probability, Springer, vol. 26(3), pages 649-665, September.

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