Cut Points on Brownian Paths

Burdzy, Krzysztof

Ann. Probab., Tome 17 (1989) no. 4, p. 1012-1036 / Harvested from Project Euclid

Résumé

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.

Publié le : 1989-07-14
Classification: Brownian motion, cut points, fractal, random fractal, 60J65, 60G17

@article{1176991254,
     author = {Burdzy, Krzysztof},
     title = {Cut Points on Brownian Paths},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 1012-1036},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991254}
}

Burdzy, Krzysztof. Cut Points on Brownian Paths. Ann. Probab., Tome 17 (1989) no. 4, pp.  1012-1036. http://gdmltest.u-ga.fr/item/1176991254/