Abstract
Let $W^{(N, d)}$ be the $N$-parameter Wiener process with values in $R^d$. It is shown that almost all sample functions of $W^{(N, d)}$ have dimensional number $2N$ and zero $2N$-measure when $d \geqq 2N$. Our results extend earlier ones of Taylor for $N = 1$.
Citation
Lanh Tat Tran. "The Hausdorff Dimension of the Range of the $N$-Parameter Wiener Process." Ann. Probab. 5 (2) 235 - 242, April, 1977. https://doi.org/10.1214/aop/1176995848
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