The fine structure of the stationary distribution for a simple Markov process

TL;DR

This paper investigates the fractal characteristics of the stationary distribution of a simple Markov process on the real line, providing bounds on its Hausdorff dimension and multifractal spectrum, along with numerical estimation methods.

Contribution

It introduces bounds for the Hausdorff dimension and multifractal spectrum of the stationary distribution, and proposes a numerical estimation approach.

Findings

Bounds for the Hausdorff dimension of the stationary distribution.

Lower bounds for the multifractal spectrum.

A numerical method for estimating these bounds.

Abstract

We study the fractal properties of the stationary distrubtion {\pi} for a simple Markov process on R. We will give bounds for the Hausdorff dimension of {\pi}, and lower bounds for the multifractal spectrum of {\pi}. Additionally, we will provide a method for numerically estimating these bounds.