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February, 1975 The Hausdorff Dimensions of the Graph and Range of $N$-Parameter Brownian Motion in $d$-Space
Lane Yoder
Ann. Probab. 3(1): 169-171 (February, 1975). DOI: 10.1214/aop/1176996458

Abstract

The paper extends results of Levy and Taylor from one-parameter Brownian motion to the multiparameter case. The following theorem is proved. For $N$-parameter Brownian motion in $d$-space, the Hausdorff dimensions of the graph and range are a.s. $\min\{2N, N + d/2\}$ and $\min\{2N, d\}$ respectively.

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Lane Yoder. "The Hausdorff Dimensions of the Graph and Range of $N$-Parameter Brownian Motion in $d$-Space." Ann. Probab. 3 (1) 169 - 171, February, 1975. https://doi.org/10.1214/aop/1176996458

Information

Published: February, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0321.60060
MathSciNet: MR359033
Digital Object Identifier: 10.1214/aop/1176996458

Subjects:
Primary: 60G17

Keywords: capacity , Hausdorff dimension

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 1 • February, 1975
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