How porous is the graph of brownian motion?

J. T. Cox; Philip S. Griffin

doi:10.1090/S0002-9947-1991-1013328-0

How porous is the graph of brownian motion?

J. T. Cox, Philip S. Griffin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	119-140
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	325
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1991-1013328-0
State	Published - May 1991

Keywords

Arcsine law
Brownian motion
Duality
Hausdorff dimension
Porous sets

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-1991-1013328-0

Cite this

@article{506670fe0c3548c895918968f4a08df6,

title = "How porous is the graph of brownian motion?",

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.",

keywords = "Arcsine law, Brownian motion, Duality, Hausdorff dimension, Porous sets",

author = "Cox, {J. T.} and Griffin, {Philip S.}",

year = "1991",

month = may,

doi = "10.1090/S0002-9947-1991-1013328-0",

language = "English (US)",

volume = "325",

pages = "119--140",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",