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
Rights
Copyright © 2021 Elsevier B.V. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.spl.2021.109300.
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