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arXiv · 1011.5043

Hausdorff and packing dimensions of the images of random fields

Narn-Rueih Shieh·Yimin Xiao
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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 $μ$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of the image measure $μ_X$ 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.

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Narn-Rueih Shieh, Yimin Xiao. 2010-11-23. Hausdorff and packing dimensions of the images of random fields. https://doi.org/10.3150/09-bej244

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