Let $W^{(N, d)}$ be the $N$-parameter Wiener process with values in $R^d$. It is shown that almost all sample functions of $W^{(N, d)}$ have dimensional number $2N$ and zero $2N$-measure when $d \geqq 2N$. Our results extend earlier ones of Taylor for $N = 1$.
Publié le : 1977-04-14
Classification:
Wiener process,
capacity,
Hausdorff dimension,
60G15,
60G17
@article{1176995848,
author = {Tran, Lanh Tat},
title = {The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 235-242},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995848}
}
Tran, Lanh Tat. The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process. Ann. Probab., Tome 5 (1977) no. 6, pp. 235-242. http://gdmltest.u-ga.fr/item/1176995848/