Open Access
Translator Disclaimer
2021 Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods
Christophe Andrieu, Paul Dobson, Andi Q. Wang
Author Affiliations +
Electron. J. Probab. 26: 1-26 (2021). DOI: 10.1214/21-EJP643


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.

Funding Statement

Research of CA supported by EPSRC grants Bayes4Health, ‘New Approaches to Bayesian Data Science: Tackling Challenges from the Health Sciences’ (EP/R018561/1) and ‘CoSInES (COmputational Statistical INference for Engineering and Security)’ (EP/R034710/1). Research of PD supported by the research programme ‘Zigzagging through computational barriers’ with project number 016.Vidi.189.043, financed by the Dutch Research Council (NWO). Research of AQW supported by EPSRC grant CoSInES (EP/R034710/1).


We are very grateful to the anonymous reviewer, whose helpful remarks have improved the paper. We would like to thank the Heilbronn Institute for Mathematical Research Research for funding the Hypocoercivity Workshop held at the University of Bristol, March 2020, which initiated this research. We would like to thank Joris Bierkens, Anthony Lee and Sam Power for interesting discussions related to this work.


Download Citation

Christophe Andrieu. Paul Dobson. Andi Q. Wang. "Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods." Electron. J. Probab. 26 1 - 26, 2021.


Received: 3 December 2020; Accepted: 4 May 2021; Published: 2021
First available in Project Euclid: 1 June 2021

Digital Object Identifier: 10.1214/21-EJP643

Primary: 60J25 , 65C05

Keywords: hypocoercivity , Markov chain Monte Carlo , piecewise-deterministic Markov process , subgeometric convergence


Vol.26 • 2021
Back to Top