Solving Poisson's equation for Wasserstein contractive Markov chains
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908847243788288 |
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| author | Hofstadler, Julian |
| author_facet | Hofstadler, Julian |
| contents | 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 $L^p$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solving Poisson's equation for Wasserstein contractive Markov chains Hofstadler, Julian Probability 60J05, 60J22, 65C05 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 $L^p$ 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. |
| title | Solving Poisson's equation for Wasserstein contractive Markov chains |
| topic | Probability 60J05, 60J22, 65C05 |
| url | https://arxiv.org/abs/2602.19119 |