Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods

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Abstract

We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to equilibrium. We make use of weak Poincar\'e inequalities, as developed in the work of [Grothaus and Wang (2019)], the ideas of which we adapt to the PDMPs of interest. On the way we report largely potential-independent approaches to bounding explicitly solutions of the Poisson equation of the Langevin diffusion and its first and second derivatives, required here to control various terms arising in the application of the hypocoercivity result.
Original languageEnglish
Article number78
Number of pages26
JournalElectronic Journal of Probability
Volume26
Early online date1 Jun 2021
DOIs
Publication statusPublished - 1 Jun 2021

Bibliographical note

33 pages, 1 figure. Minor revisions made

Keywords

  • hypocoercivity
  • Markov chain Monte Carlo
  • piecewise-deterministic Markov process
  • subgeometric convergence

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