Open Access
August 2019 Ergodicity of the zigzag process
Joris Bierkens, Gareth O. Roberts, Pierre-André Zitt
Ann. Appl. Probab. 29(4): 2266-2301 (August 2019). DOI: 10.1214/18-AAP1453


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 (Markov Chains and Stochastic Stability (2009) Cambridge Univ. Press; Adv. in Appl. Probab. 25 (1993) 487–517). 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.


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Joris Bierkens. Gareth O. Roberts. Pierre-André Zitt. "Ergodicity of the zigzag process." Ann. Appl. Probab. 29 (4) 2266 - 2301, August 2019.


Received: 1 December 2017; Revised: 1 October 2018; Published: August 2019
First available in Project Euclid: 23 July 2019

zbMATH: 07120709
MathSciNet: MR3983339
Digital Object Identifier: 10.1214/18-AAP1453

Primary: 60F05
Secondary: 65C05

Keywords: central limit theorem , ergodicity , exponential ergodicity , irreducibility , Piecewise deterministic Markov process

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.29 • No. 4 • August 2019
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