Cores for piecewise-deterministic Markov processes used in Markov chain Monte Carlo

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