Abstract
We show that if $2N \leq d$, then with probability 1 the Brownian sheet $W: R^N_+ \rightarrow R^d$ satisfies $\forall$ Borel set $E, \dim W(E) = 2 \dim E$.
Citation
T. S. Mountford. "Uniform Dimension Results for the Brownian Sheet." Ann. Probab. 17 (4) 1454 - 1462, October, 1989. https://doi.org/10.1214/aop/1176991165
Information
Published: October, 1989
First available in Project Euclid: 19 April 2007
zbMATH: 0695.60077
MathSciNet: MR1048937
Digital Object Identifier: 10.1214/aop/1176991165
Subjects:
Primary:
60G15
Secondary:
60G17
,
60J30
Keywords:
Brownian sheet
,
Hausdorff dimension
Rights: Copyright © 1989 Institute of Mathematical Statistics
