Generalized dimensions of images of measures under Gaussian processes
Abstract
We show that for certain Gaussian random processes and fields X:RN→Rd, Dq(μx) = min {d, 1/α Dq (μ)} a.s., for an index α which depends on Hölder properties and strong local nondeterminism of X, where q>1, where Dq denotes generalized q-dimension μX is the image of the measure μ under X. In particular this holds for index-α fractional Brownian motion, for fractional Riesz–Bessel motions and for certain infinity scale fractional Brownian motions.
Citation
Falconer , K & Xiao , Y 2014 , ' Generalized dimensions of images of measures under Gaussian processes ' , Advances in Mathematics , vol. 252 , pp. 492-517 . https://doi.org/10.1016/j.aim.2013.11.002
Publication
Advances in Mathematics
Status
Peer reviewed
ISSN
0001-8708Type
Journal article
Description
26 pagesCollections
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