On random topological Markov chains with big images and preimages
Manuel Stadlbauer

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.
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