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January 2000 A functional LIL for symmetric stable processes
Xia Chen, James Kuelbs, Wenbo Li
Ann. Probab. 28(1): 258-276 (January 2000). DOI: 10.1214/aop/1019160119

Abstract

A functional law of the iterated logarithm is obtained for symmetric stable processes with stationaryindependent increments.This extends the classical liminf results of Chung for Brownian motion, and of Taylor for such remaining processes. It also extends an earlier result of Wichura on Brownian motion.Proofs depend on small ball probability estimates and yield the small ball probabilities of the weighted sup-norm for these processes.

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Xia Chen. James Kuelbs. Wenbo Li. "A functional LIL for symmetric stable processes." Ann. Probab. 28 (1) 258 - 276, January 2000. https://doi.org/10.1214/aop/1019160119

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60026
MathSciNet: MR1756005
Digital Object Identifier: 10.1214/aop/1019160119

Subjects:
Primary: 60B17 , 60G17 , 60J30

Keywords: Functional LIL , small ball probabilities , Symmetric stable processes

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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