Polynomial Convergence Rates of Piecewise Deterministic Markov Processes

Polynomial Convergence Rates of Piecewise Deterministic Markov Processes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Polynomial Convergence Rates of Piecewise Deterministic Markov Processes Gareth O. Roberts, Jeffrey S. Rosenthal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1995506/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 31 Jan, 2023 Read the published version in Methodology and Computing in Applied Probability → Version 1 posted 4 You are reading this latest preprint version Abstract We consider piecewise-deterministic Markov processes such as the Bouncy Particle sampler, on target densities with polynomial tails. Using direct drift condition methods, we provide bounds on the polynomial order of the processes' convergence rate to stationary, on both one-dimensional and high-dimensional state spaces, in both total variation distance and f -norm. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 31 Jan, 2023 Read the published version in Methodology and Computing in Applied Probability → Version 1 posted Editorial decision: Major revision 25 Oct, 2022 Editor assigned by journal 25 Oct, 2022 Submission checks completed at journal 30 Aug, 2022 First submitted to journal 24 Aug, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1995506","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":132671689,"identity":"e1b9bf3f-1f82-4e5f-9e56-648729446f57","order_by":0,"name":"Gareth O. Roberts","email":"","orcid":"","institution":"University of Warwick","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Gareth","middleName":"O.","lastName":"Roberts","suffix":""},{"id":132671690,"identity":"01dfbe3c-352b-49b7-ab18-811f0b987545","order_by":1,"name":"Jeffrey S. 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