Solving Poisson's equation for Wasserstein contractive Markov chains
Probability
2026-02-24 v1
Abstract
We study Poisson's equation in the context of general state space Markov chains. For chains satisfying a contraction assumption w.r.t. a Wasserstein distance, we show that a solution exists for Lipschitz functions and investigate its regularity properties. If the kernel is additionally reversible we are also able to show that solutions for functions exist. Combining our findings with Doob's inequalities for martingales we derive maximal inequalities for contractive Markov chains. A number of examples is provided to demonstrate the applicability of our results, in particular in the context of Markov chain Monte Carlo methods.
Cite
@article{arxiv.2602.19119,
title = {Solving Poisson's equation for Wasserstein contractive Markov chains},
author = {Julian Hofstadler},
journal= {arXiv preprint arXiv:2602.19119},
year = {2026}
}
Comments
35 pages