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An extreme-value analysis of the LIL for Brownian motion. (English) Zbl 1112.60064

Summary: 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 D. A. Darling and P. Erdős [Duke Math. J. 23, 143–155 (1956; Zbl 0070.13806)].

MSC:

60J65 Brownian motion
60F05 Central limit and other weak theorems

Citations:

Zbl 0070.13806
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