ERGODICITY OF THE ZIGZAG PROCESS

• 成果类型: Article
• 署名作者: Bierkens, Joris; Roberts, Gareth O.; Zitt, Pierre-Andre
• 署名单位: Delft University of Technology; University of Warwick; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1453
• 发表日期: 2019
• 页码: 2266-2301
• 关键词: markovian processes; variance reduction; STABILITY; discrete; criteria; limit

摘要

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 (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.