English

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 LpL^p 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.

Keywords

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

R2 v1 2026-07-01T10:46:10.199Z