Hausdorff and packing dimensions of the images of random fields

Abstract

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 Lévy fields and the Rosenblatt process.

Published in at http://dx.doi.org/10.3150/09-BEJ244 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Analysis of the Rosenblatt process