Generalized dimensions of images of measures under Gaussian processes

Kenneth Falconer, Yimin Xiao

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
3 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)492-517
Number of pages26
JournalAdvances in Mathematics
Publication statusPublished - 15 Feb 2014


  • Gaussian process
  • Local nondeterminism
  • Generalised dimension
  • Fractional Brownian


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