Generalized dimensions of images of measures under Gaussian processes
Probability
2013-11-25 v2
Abstract
We show that for certain Gaussian random processes and fields X:R^N to R^d, D_q(mu_X) = min{d, D_q(mu)/alpha} a.s. for an index alpha which depends on Holder properties and strong local nondeterminism of X, where q>1, where D_q denotes generalized q-dimension and where mu_X is the image of the measure mu under X. In particular this holds for index-alpha fractional Brownian motion, for fractional Riesz-Bessel motions and for certain infinity scale fractional Brownian motions.
Keywords
Cite
@article{arxiv.1212.2383,
title = {Generalized dimensions of images of measures under Gaussian processes},
author = {Kenneth Falconer and Yimin Xiao},
journal= {arXiv preprint arXiv:1212.2383},
year = {2013}
}
Comments
26 pages