The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space
Tran, Lanh Tat
Ann. Probab., Tome 7 (1979) no. 6, p. 532-536 / Harvested from Project Euclid
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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.
Publié le : 1979-06-14
Classification:  Brownian motion,  Hausdorff dimension,  stationary,  60G15,  60G17 
@article{1176995053,
     author = {Tran, Lanh Tat},
     title = {The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space},
     journal = {Ann. Probab.},
     volume = {7},
     number = {6},
     year = {1979},
     pages = { 532-536},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995053}
}

Tran, Lanh Tat. The Range of Levy's $N$-Parameter Brownian Motion in $d$-Space. Ann. Probab., Tome 7 (1979) no. 6, pp.  532-536. http://gdmltest.u-ga.fr/item/1176995053/