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Small deviations for stable processes via compactness properties of the parameter set

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  • Aurzada, Frank

Abstract

We establish a general lower bound for the small deviations of [alpha]-stable processes in terms of the metric entropy behaviour w.r.t. the Dudley metric. This generalises work by Talagrand [1993. New Gaussian estimates for enlarged balls. Geom. Funct. Anal. 3, 502-526] for Gaussian processes and yields new bounds for stable self-similar processes.

Suggested Citation

  • Aurzada, Frank, 2008. "Small deviations for stable processes via compactness properties of the parameter set," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 577-581, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:577-581
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