Ergodicity of the zigzag process

Joris Bierkens, Gareth O. Roberts, Pierre-Andre Zitt

Research output: Contribution to journalArticleScientificpeer-review

36 Citations (Scopus)


The zigzag process is a piecewise deterministic Markov process which can be used in aMCMC 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.

Original languageEnglish
Pages (from-to)2266-2301
Number of pages36
JournalAnnals of Applied Probability
Issue number4
Publication statusPublished - 2019


  • Central limit theorem
  • Ergodicity
  • Exponential ergodicity
  • Irreducibility
  • Piecewise deterministic Markov process


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