Box-counting dimension and differentiability of box-like statistically self-affine functions
Classical Analysis and ODEs
2023-06-21 v1 Probability
Abstract
We consider a class of "box-like" statistically self-affine functions, and compute the almost-sure box-counting dimension of their graphs. Furthermore, we consider the differentiability of our functions, and prove that, depending on an explicitly computable functional of the model, they are almost surely either differentiable almost everywhere or non-differentiable almost everywhere.
Keywords
Cite
@article{arxiv.2208.00035,
title = {Box-counting dimension and differentiability of box-like statistically self-affine functions},
author = {Pieter Allaart and Taylor Jones},
journal= {arXiv preprint arXiv:2208.00035},
year = {2023}
}
Comments
25 pages, 4 figures