Hausdorff and packing dimensions of the images of random fields

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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