On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms

Abstract

We establish ${\mathit{L}}^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard ${\mathit{L}}^2$ energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.