Hausdorff and packing dimensions of the images of random fields
Resource
Bernoulli, 16(4), 926-952
Journal
Bernoulli
Pages
926-952
Date Issued
2010
Date
2010
Author(s)
Shieh, Narn-Rueih
Xiao, Yimin
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.
Type
journal article
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