The Annals of Probability

The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space

Lanh Tat Tran

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Abstract

Let $B^{(N,d)}$ be Levy's $N$-parameter Brownian motion in $d$-space. It is shown that almost surely $B^{(N,d)}$ doubles the Hausdorff dimension of every Borel set in the parameter space when $d \geqslant 2N$. The dimension of the range of $B$ is also determined in this case.

Article information

Source
Ann. Probab. Volume 7, Number 3 (1979), 532-536.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995053

Digital Object Identifier
doi:10.1214/aop/1176995053

Mathematical Reviews number (MathSciNet)
MR528330

Zentralblatt MATH identifier
0398.60039

JSTOR
links.jstor.org

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

Keywords
Brownian motion Hausdorff dimension stationary

Citation

Tran, Lanh Tat. The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space. Ann. Probab. 7 (1979), no. 3, 532--536. doi:10.1214/aop/1176995053. https://projecteuclid.org/euclid.aop/1176995053


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