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.
Citation
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
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