Hypocoercivity of piecewise deterministic Markov process-Monte Carlo

In this work, we establish L2-exponential convergence for a broad class of piecewise deterministic Markov processes recently proposed in the context process Monte Carlo methods and covering particular randomized Hamiltonian (Trans. Amer. Math. Soc. 367 (2015) 3807–3828; Ann. Appl. Probab. 27 (2017) 2159–2194), zig-zag (Ann. Statist. 47 (2019) 1288–1320) bouncy particle Sampler (Phys. Rev. E 85 (2012) 026703; J. Assoc. 113 (2018) 855–867). The kernel symmetric part generator such is nontrivial, follow ideas introduced (C. R. Acad. Sci. Paris 347 (2009) 511–516; Trans. 3807–3828) to develop rigorous framework hypocoercivity fairly general unifying set-up, while deriving tractable estimates constants involved terms parameters dynamics. As by-product characterize scaling properties these algorithms with respect dimension classes problems, therefore providing some theoretical evidence support their practical relevance.