On random topological Markov chains with big images and preimages

TL;DR

This paper introduces a new relative 'big images and preimages' property for random topological Markov chains, enabling a generalized Ruelle-Perron-Frobenius theorem for certain potentials.

Contribution

It develops a relative version of the 'big images and preimages' property and proves a corresponding Ruelle-Perron-Frobenius theorem for random topological Markov chains.

Findings

Established a relative 'big images and preimages' property.

Proved a generalized Ruelle-Perron-Frobenius theorem.

Applicable to summable and locally Hölder continuous potentials.

Abstract

We introduce a relative notion of the 'big images and preimages'-property for random topological Markov chains. This then implies that a relative version of the Ruelle-Perron-Frobenius theorem holds with respect to summable and locally Hoelder continuous potentials.