Intermediate dimension of images of sequences under fractional Brownian motion

We show that the almost sure theta-intermediate dimension of the image of the set F-p = {0, 1, 1/2p, 1/3p, ...} under index -h fractional Brownian motion is theta/ph+theta , a value that is smaller than that given by directly applying the Holder bound for fractional Brownian motion. In particular this establishes the box-counting dimension of these images. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This research demonstrates that the almost sure theta-intermediate dimension of the image of the set F-p under index -h fractional Brownian motion is theta/ph+theta, a value smaller than that obtained by directly applying the Holder bound for fractional Brownian motion, thus establishing the box-counting dimension of these images.