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, self-similar stable random fields with stationary increments, real harmonizable fractional Lévy fields and the Rosenblatt process.
Publié le : 2010-11-15
Classification:
Hausdorff dimension,
images,
packing dimension,
packing dimension profiles,
real harmonizable fractional Lévy motion,
Rosenblatt process,
self-similar stable random fields
@article{1290092890,
author = {Shieh, Narn-Rueih and Xiao, Yimin},
title = {Hausdorff and packing dimensions of the images of random fields},
journal = {Bernoulli},
volume = {16},
number = {1},
year = {2010},
pages = { 926-952},
language = {en},
url = {http://dml.mathdoc.fr/item/1290092890}
}
Shieh, Narn-Rueih; Xiao, Yimin. Hausdorff and packing dimensions of the images of random fields. Bernoulli, Tome 16 (2010) no. 1, pp. 926-952. http://gdmltest.u-ga.fr/item/1290092890/