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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

How porous is the graph of Brownian motion?


Authors: J. T. Cox and Philip S. Griffin
Journal: Trans. Amer. Math. Soc. 325 (1991), 119-140
MSC: Primary 60J65
DOI: https://doi.org/10.1090/S0002-9947-1991-1013328-0
MathSciNet review: 1013328
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Abstract: We prove that the graph of Brownian motion is almost surely porous, and determine the Hausdorff dimension of sets with a given porosity index. In particular we show that the porosity index of the graph is $ {\gamma _0} \doteq 0.6948$.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1013328-0
Keywords: Brownian motion, arcsine law, porous sets, Hausdorff dimension
Article copyright: © Copyright 1991 American Mathematical Society