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,1αDq(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 and where 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.