Yet Another Quantitative Harris Theorem

Abstract: In this paper we develop a quantitative Harris theorem with effective control over the constants. A benefit of our methodology is the decoupling of the small set and Lyapunov-Foster Drift conditions. Our methodology allows any small set and any set in the Lyapunov-Foster condition as long as the second satisfies a so-called ``quantitative petiteness" condition. The theorem relies on a novel proof of a quantitative Kendall-type theorem which is inspired by the techniques of Markov Chains on general state spaces. We give an application of the technique to the Markov chain approximation of mixing processes.