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

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.Gaussian processes Linear fractional stable motion Metric entropy Self-similar processes Small deviation Stable processes