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Article Dans Une Revue The Annals of Applied Probability Année : 2019

Ergodicity of the zigzag process

Résumé

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 [MT93b; MT09]. 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. MSC 2010 subject classifications: Primary 60F05; secondary 65C05.
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Dates et versions

hal-01671825 , version 1 (22-12-2017)
hal-01671825 , version 2 (02-10-2019)

Identifiants

Citer

Joris Bierkens, Gareth Roberts, Pierre-André Zitt. Ergodicity of the zigzag process. The Annals of Applied Probability, 2019, 29 (4), pp.2266-2301. ⟨10.1214/18-AAP1453⟩. ⟨hal-01671825v2⟩
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