Nonuniform Markov geometric measures

TL;DR

This paper extends the understanding of the measure-theoretic properties of Markov geometric series, including absolute continuity and singularity, and explores their applications in fractal geometry.

Contribution

It generalizes previous results to nonuniform Markov processes and applies these findings to fractal geometry.

Findings

Characterization of absolute continuity and singularity in nonuniform Markov series

Extension of Fan and Zhang's results to broader Markov processes

Application of measure properties to fractal geometry analysis

Abstract

We generalize results of Fan and Zhang [6] on absolute continuity and singularity of the golden Markov geometric series to nonuniform stochastic series given by arbitrary Markov process. In addition we describe an application of these results in fractal geometry.