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Quantitative contraction rates for Markov chains on general state spaces
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Eberle, Andreas and Majka, Mateusz B. (2019) Quantitative contraction rates for Markov chains on general state spaces. Electronic Journal of Probability, 24 (26). doi:10.1214/19-EJP287 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/19-EJP287
Abstract
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich (L1 Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently been derived by combining appropriate couplings with carefully designed Kantorovich distances. In this paper, we partially carry over this approach from diffusions to Markov chains. We derive quantitative lower bounds on contraction rates for Markov chains on general state spaces that are powerful if the dynamics is dominated by small local moves. For Markov chains on Rd with isotropic transition kernels, the general bounds can be used efficiently together with a coupling that combines maximal and reflection coupling. The results are applied to Euler discretizations of stochastic differential equations with non-globally contractive drifts, and to the Metropolis adjusted Langevin algorithm for sampling from a class of probability measures on high dimensional state spaces that are not globally log-concave
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Markov processes | |||||||||||||||
| Journal or Publication Title: | Electronic Journal of Probability | |||||||||||||||
| Publisher: | University of Washington. Dept. of Mathematics | |||||||||||||||
| ISSN: | 1083-6489 | |||||||||||||||
| Official Date: | 26 March 2019 | |||||||||||||||
| Dates: |
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| Volume: | 24 | |||||||||||||||
| Number: | 26 | |||||||||||||||
| DOI: | 10.1214/19-EJP287 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||
| Date of first compliant deposit: | 1 May 2019 | |||||||||||||||
| Date of first compliant Open Access: | 7 May 2019 | |||||||||||||||
| RIOXX Funder/Project Grant: |
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