The Hausdorff Dimensions of the Graph and Range of $N$-Parameter Brownian Motion in $d$-Space
Yoder, Lane
Ann. Probab., Tome 3 (1975) no. 6, p. 169-171 / Harvested from Project Euclid
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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.
Publié le : 1975-02-14
Classification:  Hausdorff dimension,  capacity,  60G17 
@article{1176996458,
     author = {Yoder, Lane},
     title = {The Hausdorff Dimensions of the Graph and Range of $N$-Parameter Brownian Motion in $d$-Space},
     journal = {Ann. Probab.},
     volume = {3},
     number = {6},
     year = {1975},
     pages = { 169-171},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996458}
}

Yoder, Lane. The Hausdorff Dimensions of the Graph and Range of $N$-Parameter Brownian Motion in $d$-Space. Ann. Probab., Tome 3 (1975) no. 6, pp.  169-171. http://gdmltest.u-ga.fr/item/1176996458/