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arXiv · 1712.09875

Ergodicity of the zigzag process

Joris Bierkens·Gareth Roberts·Pierre-André Zitt
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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.

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Joris Bierkens, Gareth Roberts, Pierre-André Zitt. 2019-01-18. Ergodicity of the zigzag process. https://doi.org/10.1214/18-aap1453

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