Polynomial Convergence Rates of Piecewise Deterministic Markov Processes

Abstract

We consider piecewise-deterministic Markov processes such as the Bouncy Particle sampler, on target densities with polynomial tails. Using direct drift condition methods, we provide bounds on the polynomial order of the processes’ convergence rate to stationary, on both one-dimensional and high-dimensional state spaces, in both total variation distance and f-norm.