Intermediate dimension of images of sequences under fractional Brownian motion
Abstract
We show that the almost sure θ-intermediate dimension of the image of the set Fp ={0, 1,1/2p,1/3p,...} under index-h fractional Brownian motion is θ/(ph+θ), a value that is smaller than that given by directly applying the Hölder bound for fractional Brownian motion. In particular this establishes the box-counting dimension of these images.
Citation
Falconer , K J 2022 , ' Intermediate dimension of images of sequences under fractional Brownian motion ' , Statistics and Probability Letters , vol. 182 , 109300 . https://doi.org/10.1016/j.spl.2021.109300
Publication
Statistics and Probability Letters
Status
Peer reviewed
ISSN
0167-7152Type
Journal article
Collections
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