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Ergodicity of the zigzag process
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Bierkins, Joris, Roberts, Gareth O. and Zitt, Pierre-Andre (2019) Ergodicity of the zigzag process. Annals of Applied Probability, 29 (4). 2266-2301 . doi:10.1214/18-AAP1453 ISSN 1050-5164.
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Official URL: https://doi.org/10.1214/18-AAP1453
Abstract
The zigzag process is a Piecewise Deterministic Markov Process which can be used in a MCMC framework to sample from a given target distribution. We prove the convergence of this process to its target under very weak assumptions, and establish a central limit theorem for empirical averages under stronger assumptions on the decay of the target measure. We use the classical ``Meyn-Tweedie'' approach. The main difficulty turns out to be the proof that the process can indeed reach all the points in the space, even if we consider the minimal switching rates.
| 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, Monte Carlo method | |||||||||||||||
| Journal or Publication Title: | Annals of Applied Probability | |||||||||||||||
| Publisher: | Institute of Mathematical Statistics | |||||||||||||||
| ISSN: | 1050-5164 | |||||||||||||||
| Official Date: | August 2019 | |||||||||||||||
| Dates: |
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| Volume: | 29 | |||||||||||||||
| Number: | 4 | |||||||||||||||
| Page Range: | 2266-2301 | |||||||||||||||
| DOI: | 10.1214/18-AAP1453 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
| Date of first compliant deposit: | 16 January 2019 | |||||||||||||||
| Date of first compliant Open Access: | 16 January 2019 | |||||||||||||||
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