Ergodicity of the zigzag process

Journal article (2019)

Authors

G.N.J.C. Bierkens Statistics -

Gareth Roberts University of Warwick

Pierre-Andre Zitt Université Paris-Est

Research Group

Statistics () (TU Delft)

Central limit theorem Exponential ergodicity Piecewise deterministic Markov process Ergodicity Irreducibility

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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

Abstract

The zigzag process is a piecewise deterministic Markov process which can be used in aMCMC 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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