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Probab."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (higher states have higher transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained with the use of order-theoretic mixing conditions. We complement these results by providing quantitative bounds on deviations between distributions. We also show that well-known total variation bounds can be recovered as a special case.<\/jats:p>","DOI":"10.1017\/jpr.2025.10055","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T10:52:12Z","timestamp":1768992732000},"page":"798-810","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Quantitative convergence rates for stochastically monotone Markov chains"],"prefix":"10.1017","volume":"63","author":[{"given":"Takashi","family":"Kamihigashi","sequence":"first","affiliation":[{"name":"Kobe University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6716-0111","authenticated-orcid":false,"given":"John","family":"Stachurski","sequence":"additional","affiliation":[{"name":"Australian National University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"S0021900225100557_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2010.03.019"},{"key":"S0021900225100557_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2020.07.003"},{"key":"S0021900225100557_ref24","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v7-1054"},{"key":"S0021900225100557_ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0021-1_7"},{"key":"S0021900225100557_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995392"},{"key":"S0021900225100557_ref26","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177700153"},{"key":"S0021900225100557_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-020-03834-w"},{"key":"S0021900225100557_ref2","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v18-1720"},{"key":"S0021900225100557_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.euroecorev.2005.11.008"},{"key":"S0021900225100557_ref18","unstructured":"[18] Lindvall, T. (2002). Lectures on the Coupling Method. Dover."},{"key":"S0021900225100557_ref11","doi-asserted-by":"crossref","unstructured":"[11] Gaudio, J. , Amin, S. and Jaillet, P. (2018). Exponential convergence rates for stochastically ordered Markov processes with random initial conditions. arXiv preprint arXiv:1810.07732v1.","DOI":"10.1016\/j.sysconle.2019.104515"},{"key":"S0021900225100557_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s101140000049"},{"key":"S0021900225100557_ref15","doi-asserted-by":"publisher","DOI":"10.3982\/TE1367"},{"key":"S0021900225100557_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jet.2017.11.004"},{"key":"S0021900225100557_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/25-AAP2184"},{"key":"S0021900225100557_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2019.2"},{"key":"S0021900225100557_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-19071-2_104-1"},{"key":"S0021900225100557_ref9","unstructured":"[9] Foss, S. and Scheutzow, M. (2024). Compressibility and stochastic stability of monotone Markov chains. arXiv preprint arXiv:2403.15259v1."},{"key":"S0021900225100557_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2022.109830"},{"key":"S0021900225100557_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2009.10.001"},{"key":"S0021900225100557_ref4","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP922"},{"key":"S0021900225100557_ref3","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176991694"},{"key":"S0021900225100557_ref23","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476548"},{"key":"S0021900225100557_ref13","doi-asserted-by":"publisher","DOI":"10.1090\/noti2253"},{"key":"S0021900225100557_ref20","doi-asserted-by":"publisher","DOI":"10.1561\/0400000003"},{"key":"S0021900225100557_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/21-AIHP1195"},{"key":"S0021900225100557_ref19","doi-asserted-by":"publisher","DOI":"10.1214\/aoap\/1034968072"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900225100557","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:37:12Z","timestamp":1782290232000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0021900225100557\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,21]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0021900225100557"],"URL":"https:\/\/doi.org\/10.1017\/jpr.2025.10055","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,21]]},"assertion":[{"value":"\u00a9 The Author(s), 2026. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}