Small Deviations of Stable Processes via Metric Entropy
| Author(s) | Li, Wenbo | |
| Author(s) | Linde, W. | |
| Date Accessioned | 2005-02-17T16:30:44Z | |
| Date Available | 2005-02-17T16:30:44Z | |
| Publication Date | 2002 | |
| Abstract | Let X = (X(t))t 2 T be a symmetric {stable, 0 < < 2, process with paths in the dual E of a certain Banach space E. Then there exists a (bounded, linear) operator u from E into some L (S; ˙) generating X in a canonical way. The aim of this paper is to compare the degree of compactness of u with the small deviation (ball) behavior of °(") =...In particular, we prove that a lower bound for the metric entropy of u implies a lower bound for °(") under an additional assumption on E. As applications we obtain lower small deviation estimates for weighted {stable Levy motions, linear fractional {stable motions and d{dimensional {stable Levy sheets. Our results rest upon an integral representation of L {valued operators as well as on small deviation results for Gaussian processes due to Kuelbs and Li and to the authors. | en |
| Sponsor | Supported in part by NSF Grant DMS-0204513 | en |
| Extent | 276173 bytes | |
| MIME type | application/pdf | |
| URL | http://udspace.udel.edu/handle/19716/335 | |
| Language | en_US | |
| Publisher | Department of Mathematical Sciences | en |
| Part of Series | Technical Report: 2002-11 | |
| Keywords | stable processes | en |
| Keywords | small deviation | en |
| Keywords | metric entropy | en |
| dc.subject.classification | AMS: 60G52, 47B06, 60G15, 47G10 | |
| Title | Small Deviations of Stable Processes via Metric Entropy | en |
| Type | Technical Report | en |