Constructions involving interaction of Markov process's with a random environment

TL;DR

This paper introduces a new construction for Markov processes interacting with a random environment, allowing for more relaxed conditions while maintaining the ability to analyze the combined system effectively.

Contribution

It presents a novel construction method for Markov processes in random environments that requires less restrictive assumptions than previous approaches.

Findings

The new construction preserves key properties of the combined process.

It enables analysis under more general conditions.

The approach simplifies studying interactions between processes and environments.

Abstract

Recently Belopolskaya and Suhov studied Markov process's in a random environment, where the environment changes in likeness to a Markov process. Constructions were made to allow the process to "interact with the environment", this was done in such a manner that the combined process could be studied by studying the individual ones. A new construction is made which has similar properties. This construction can be carried out with more relaxed conditions than the ones previously done.