Intermediate dimension of images of sequences under fractional Brownian motion

Kenneth J. Falconer

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arXiv · 2108.12306

Intermediate dimension of images of sequences under fractional Brownian motion

Kenneth J. Falconer

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Abstract

We show that the almost sure $\theta$-intermediate dimension of the image of the set $F_p =\{0, 1,\frac{1}{2^p},\frac{1}{3^p},\ldots\}$ under index-$h$ fractional Brownian motion is $\frac{\theta}{ph+\theta}$, a value that is smaller than that given by directly applying the H\"{o}lder bound for fractional Brownian motion. In particular this establishes the box-counting dimension of these images.

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Kenneth J. Falconer. 2021-08-27. Intermediate dimension of images of sequences under fractional Brownian motion. https://arxiv.org/abs/2108.12306

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