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Generalized dimensions of images of measures under Gaussian processes

Research output: Contribution to journalArticle

Author(s)

Kenneth Falconer, Yimin Xiao

School/Research organisations

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.

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Details

Original languageEnglish
Pages (from-to)492-517
Number of pages26
JournalAdvances in Mathematics
Volume252
Early online date5 Dec 2013
DOIs
Publication statusPublished - 15 Feb 2014

    Research areas

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

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