Hausdorff and packing dimensions of the images of random fields

Details Hausdorff and packing dimensions of the images of random fields Hausdorff and packing dimensions of the images of random fields

2010-11-23

arxiv.org/abs/1011.5043v1

Bernoulli 2010, Vol. 16, No. 4, 926-952

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ244 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ244

Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of the image measure $\mu_X$ and image set $X(E)$ are determined under certain mild conditions. These results are applicable to Gaussian random fields, self-similar stable random fields with stationary increments, real harmonizable fractional L\'{e}vy fields and the Rosenblatt process.

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