English

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}
}

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26 pages