Hausdorff and packing dimensions of the images of random fields

Abstract

Let X = {X(t), t ∈ ℝN} be a random field with values in ℝd. For any finite Borel measure μ and analytic set E ⊂ ℝN, the Hausdorff and packing dimensions of the image measure μX and image set X(E) are determined under certain mild conditions. These results are applicable to Gaussian random fields, selfsimilar stable random fields with stationary increments, real harmonizable fractional Lévy fields and the Rosenblatt process. © 2010 ISI/BS.