We show fundamental properties of the Markov semigroup of recently proposed MCMC algorithms based on Piecewise-deterministic Markov processes (PDMPs) such as the Bouncy Particle Sampler, the Zig-Zag process or the Randomized Hamiltonian Monte Carlo method. Under assumptions typically satisfied in MCMC settings, we prove that PDMPs are Feller and that their generator admits the space of infinitely differentiable functions with compact support as a core. As we illustrate via martingale problems and a simplified proof of the invariance of target distributions, these results provide a fundamental tool for the rigorous analysis of these algorithms and corresponding stochastic processes.

翻译：我们展示了马尔科夫(Markov ) 半组基于Pocet-definistic Markov (PDMPs) (PDMPs) (PPMMMC) (PPPWE-deter-deministic Markov) (PDMPs) (PDMPs) (PDMPs) (PDMPs) (PDMPs) (PDMPs) (PDMPs) (PDMPs) (PPPouncy Particle Prophererer) (PPouncy Particle Problicer(Proctor) ) (Zig-Zag-Zag) (Zag-Zag) (或随机化的汉密尔密尔顿·蒙特·蒙特·卡洛(Honte Carlo) (Rol) (Randomidal) (MCDMMC) (MMCs) (MMC ) (MMC ) (M ) (M Mcs) (MMMMCs) (MC) (MC) (MC) (MC) (Mc) (PD Mc) (Mc) (M Mc) (M Mc) (MMM Mc) (M Mc) (M Mc) (M Mc) (M) (M) (M) (PM ) (M) (M) (M) (M) (M) (M) (PDM) (PDM) (PD) (PD) (PDMC) (PD) (M) (M) (M) (PDM) (M) (M) (M) (M) (M) (M) (PD) (PM) (M) (PM) (PD) (M) (PM) (PDs) (PDs) (PD) (PD) (PD) (PD) (M) (PPD) (PD) (PD) (M) (M) (M) (M) (PD) (M) (PD) (PM) (PD) (M) (PD) (M) (P