Journal
ANNALS OF APPLIED PROBABILITY
Volume 29, Issue 4, Pages 2266-2301Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-AAP1453
Keywords
Piecewise deterministic Markov process; irreducibility; ergodicity; exponential ergodicity; central limit theorem
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Funding
- European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant [614492]
- French National Research Agency [ANR-12-JS01-0006]
- EPSRC [EP/D002060/1, EP/K014463/1]
- EPSRC [EP/K014463/1, EP/R034710/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/R034710/1] Funding Source: researchfish
- Agence Nationale de la Recherche (ANR) [ANR-12-JS01-0006] Funding Source: Agence Nationale de la Recherche (ANR)
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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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