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April, 1977 The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process
Lanh Tat Tran
Ann. Probab. 5(2): 235-242 (April, 1977). DOI: 10.1214/aop/1176995848


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 $N = 1$.


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Lanh Tat Tran. "The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process." Ann. Probab. 5 (2) 235 - 242, April, 1977.


Published: April, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0366.60051
MathSciNet: MR431360
Digital Object Identifier: 10.1214/aop/1176995848

Primary: 60G15
Secondary: 60G17

Keywords: capacity , Hausdorff dimension , Wiener process

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • April, 1977
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