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We extend the hypocoercivity framework for piecewise-deterministic Markovprocess (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] toheavy-tailed target distributions, which exhibit subgeometric rates ofconvergence to equilibrium. We make use of weak Poincar\'e inequalities, asdeveloped in the work of [Grothaus and Wang (2019)], the ideas of which weadapt to the PDMPs of interest. On the way we report largelypotential-independent approaches to bounding explicitly solutions of thePoisson equation of the Langevin diffusion and its first and secondderivatives, required here to control various terms arising in the applicationof the hypocoercivity result.

Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods