Annals of Probability

The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process

Lanh Tat Tran

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Abstract

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 $N = 1$.

Article information

Source
Ann. Probab., Volume 5, Number 2 (1977), 235-242.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995848

Digital Object Identifier
doi:10.1214/aop/1176995848

Mathematical Reviews number (MathSciNet)
MR431360

Zentralblatt MATH identifier
0366.60051

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G17: Sample path properties

Keywords
Wiener process capacity Hausdorff dimension

Citation

Tran, Lanh Tat. The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process. Ann. Probab. 5 (1977), no. 2, 235--242. doi:10.1214/aop/1176995848. https://projecteuclid.org/euclid.aop/1176995848


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