How porous is the graph of brownian motion?

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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 y?0 = 0.6948.

Original languageEnglish (US)
Pages (from-to)119-140
Number of pages22
JournalTransactions of the American Mathematical Society
Volume325
Issue number1
DOIs
StatePublished - 1991

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Keywords

  • Arcsine law
  • Brownian motion
  • Duality
  • Hausdorff dimension
  • Porous sets

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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