Dimensional Properties of One-Dimensional Brownian Motion
Kaufman, Robert
Ann. Probab., Tome 17 (1989) no. 4, p. 189-193 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
For each closed set $F \subseteq \lbrack 0, 1\rbrack, \dim X(F + t) = \min(1, 2 \dim F)$ for almost all $t > 0. (X$ is one-dimensional Brownian motion). For each closed set $F \subseteq \lbrack 0, 1 \rbrack$ of dimension greater than $1/2, m(X(F + t)) > 0$ for almost all $t > 0$. These statements are true outside a single null-set in the sample space.
Publié le : 1989-01-14
Classification:  Brownian motion,  dimension,  capacity,  60J65,  28A75 
@article{1176991503,
     author = {Kaufman, Robert},
     title = {Dimensional Properties of One-Dimensional Brownian Motion},
     journal = {Ann. Probab.},
     volume = {17},
     number = {4},
     year = {1989},
     pages = { 189-193},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991503}
}

Kaufman, Robert. Dimensional Properties of One-Dimensional Brownian Motion. Ann. Probab., Tome 17 (1989) no. 4, pp.  189-193. http://gdmltest.u-ga.fr/item/1176991503/