Ergodicity of the zigzag process
Probability
2020-09-29 v2
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.
Cite
@article{arxiv.1712.09875,
title = {Ergodicity of the zigzag process},
author = {Joris Bierkens and Gareth Roberts and Pierre-André Zitt},
journal= {arXiv preprint arXiv:1712.09875},
year = {2020}
}