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Ergodicity of the zigzag process. (English) Zbl 1467.60020

Summary: 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 [S. P. Meyn and R. L. Tweedie, Adv. Appl. Probab. 25, No. 3, 487–517 (1993; Zbl 0781.60052)]. 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:

60F05 Central limit and other weak theorems
65C05 Monte Carlo methods

Citations:

Zbl 0781.60052
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References:

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