The Annals of Probability

Cut Points on Brownian Paths

Krzysztof Burdzy

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Abstract

Let $X$ be a standard two-dimensional Brownian motion. There exists a.s. $t \in (0, 1)$ such that $X(\lbrack 0, t)) \cap X((t, 1 \rbrack) = \varnothing$. It follows that $X(\lbrack 0, 1 \rbrack)$ is not homeomorphic to the Sierpinski carpet a.s.

Article information

Source
Ann. Probab., Volume 17, Number 3 (1989), 1012-1036.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991254

Digital Object Identifier
doi:10.1214/aop/1176991254

Mathematical Reviews number (MathSciNet)
MR1009442

Zentralblatt MATH identifier
0691.60069

JSTOR
links.jstor.org

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60G17: Sample path properties

Keywords
Brownian motion cut points fractal random fractal

Citation

Burdzy, Krzysztof. Cut Points on Brownian Paths. Ann. Probab. 17 (1989), no. 3, 1012--1036. doi:10.1214/aop/1176991254. https://projecteuclid.org/euclid.aop/1176991254


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