METRIC ENTROPY AND THE SMALL DEVIATION PROBLEM FOR
STABLE PROCESSES
Abstract: The famous connection between metric entropy and small deviation probabilities of
Gaussian processes was discovered by Kuelbs and Li in [6] and completed by Li and Linde in
[9]. The question whether similar connections exist for other types of processes has remained
open ever since. In [10], Li and Linde propose a first approach to this problem for stable
processes. The present article clarifies the question completely for symmetric stable
processes.
2000 AMS Mathematics Subject Classification: Primary: 60G52, 60G15; Secondary:
-.
Key words and phrases: Small deviation; lower tail probability; Gaussian processes;
stable processes; metric entropy.