Intermediate dimension of images of sequences under fractional Brownian motion

Abstract

We show that the almost sure $\theta$-intermediate dimension of the image of the set $F_p=\{0,1,\frac{1}{2^p},\frac{1}{3^p},\dots \}$ under index-$h$ fractional Brownian motion is $\frac{\theta }{ph+\theta }$, 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.

References in corpus (3)

• A uniform result for the dimension of fractional Brownian motion level sets
• Intermediate dimensions of infinitely generated attractors
• The fractal structure of elliptical polynomial spirals

Cited by in corpus (4)

• Intermediate dimensions of Bedford-McMullen carpets with applications to Lipschitz equivalence
• Generalised intermediate dimensions
• Intermediate dimensions of infinitely generated attractors
• Dimensions of popcorn-like pyramid sets