A functional LIL for symmetric stable processes

Authors
Chen, X Kuelbs, J Li, WB
Citation
X. Chen et al., A functional LIL for symmetric stable processes, ANN PROBAB, 28(1), 2000, pp. 258-276
Citations number
12
Categorie Soggetti
Mathematics
Journal title
ANNALS OF PROBABILITY
ISSN journal
00911798 → ACNP
Volume
28
Issue
1
Year of publication
2000
Pages
258 - 276
Database
ISI
SICI code
0091-1798(200001)28:1<258:AFLFSS>2.0.ZU;2-Q
Abstract
A functional law of the iterated logarithm is obtained for symmetric stable processes with stationary independent increments. This extends the classic al liminf results of Chung for Brownian motion, and of Taylor for such rema ining processes. It also extends an earlier result of Wichura on Brownian m otion. Proofs depend on small ball probability estimates and yield the smal l ball probabilities of the weighted sup-norm for these processes.