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June, 1979 The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space
Lanh Tat Tran
Ann. Probab. 7(3): 532-536 (June, 1979). DOI: 10.1214/aop/1176995053

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.

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Lanh Tat Tran. "The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space." Ann. Probab. 7 (3) 532 - 536, June, 1979. https://doi.org/10.1214/aop/1176995053

Information

Published: June, 1979
First available in Project Euclid: 19 April 2007

zbMATH: 0398.60039
MathSciNet: MR528330
Digital Object Identifier: 10.1214/aop/1176995053

Subjects:
Primary: 60G15
Secondary: 60G17

Keywords: Brownian motion , Hausdorff dimension , stationary

Rights: Copyright © 1979 Institute of Mathematical Statistics

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Vol.7 • No. 3 • June, 1979
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