ON EXPLICIT L2 -CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS

Journal Article (Journal Article)

We establish L2-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard L2 energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.

Full Text

Duke Authors

Cited Authors

  • Lu, J; Wang, L

Published Date

  • April 1, 2022

Published In

Volume / Issue

  • 32 / 2

Start / End Page

  • 1333 - 1361

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/21-AAP1710

Citation Source

  • Scopus