{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T06:46:35Z","timestamp":1784184395254,"version":"3.55.0"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,2,12]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>While the Metropolis-adjusted Langevin algorithm is a popular and widely used Markov chain Monte Carlo method, very few papers derive conditions that ensure its convergence. In particular, to the authors\u2019 knowledge, assumptions that are both easy to verify and guarantee geometric convergence, are still missing. In this work, we establish V-uniformly geometric convergence for the Metropolis-adjusted Langevin algorithm under mild assumptions about the target distribution. Unlike previous work, we only consider tail and smoothness conditions for the potential associated with the target distribution. These conditions are quite common in the Markov chain Monte Carlo literature. Finally, we pay special attention to the dependence of the bounds we derive on the step size of the Euler\u2013Maruyama discretization, which corresponds to the proposed Markov kernel of the Metropolis-adjusted Langevin algorithm.<\/jats:p>","DOI":"10.1093\/biomet\/asad060","type":"journal-article","created":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T17:17:39Z","timestamp":1696353459000},"page":"273-289","source":"Crossref","is-referenced-by-count":2,"title":["On geometric convergence for the Metropolis-adjusted Langevin algorithm under simple conditions"],"prefix":"10.1093","volume":"111","author":[{"given":"Alain","family":"Oliviero-Durmus","sequence":"first","affiliation":[{"name":"Centre Math\u00e9matiques Appliqu\u00e9es, Institut Polytechnique de Paris , Route de Saclay , 91120 Palaiseau, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2058-0693","authenticated-orcid":false,"given":"\u00c9ric","family":"Moulines","sequence":"additional","affiliation":[{"name":"Centre Math\u00e9matiques Appliqu\u00e9es, Institut Polytechnique de Paris , Route de Saclay , 91120 Palaiseau, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,10,3]]},"reference":[{"key":"2024021219292158000_asad060-B1","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1214\/EJP.v13-521","article-title":"A tail inequality for suprema of unbounded empirical processes with applications to Markov chains","volume":"13","author":"Adamczak","year":"2008","journal-title":"Electron. 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