Effective dimension of points visited by Brownian motion

Authors:
Bjørn Kjos-Hanssen;Anil Nerode
Affiliations:
Department of Mathematics, University of Hawai`i at Mnoa, Honolulu, HI 96822, USA;Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We consider the individual points on a Martin-Lof random path of Brownian motion. We show that (1) Khintchine's law of the iterated logarithm holds at almost all points; and (2) there exist points (besides the trivial example of the origin) having effective dimension