An Extreme-Value Analysis of the LIL for Brownian Motion

Davar Khoshnevisan (University of Utah, USa)
David A. Levin (University of Oregon, USA)
Zhan Shi (Université Paris VI, France)

Abstract


We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also proves, in a paragraph, the classical theorem of Darling and Erdős (1956).

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Pages: 196-206

Publication Date: September 30, 2005

DOI: 10.1214/ECP.v10-1154

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