Subgeometric hypocoercivity for piecewise-deterministic markov process monte carlo methods

Christophe Andrieu, Paul Dobson, Andi Q. Wang

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Abstract

We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [2] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to equilibrium. We make use of weak Poincaré inequalities, as developed in the work of [15], 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
Pages (from-to)1-26
Number of pages26
JournalElectronic Journal of Probability
Volume26
DOIs
Publication statusPublished - 2021

Keywords

  • Hypocoercivity
  • Markov chain Monte Carlo
  • Piecewise-deterministic Markov process
  • Subgeometric convergence

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