Infinite dimensional Piecewise Deterministic Markov Processes

Paul Dobson, Joris Bierkens*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

36 Downloads (Pure)

Abstract

In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the Zig-Zag Sampler and the Boomerang Sampler. In order to do so we provide an abstract infinite dimensional framework for Piecewise Deterministic Markov Processes (PDMPs) with unbounded event intensities. We further develop exponential convergence to equilibrium of the infinite dimensional Boomerang Sampler, using hypocoercivity techniques. Furthermore we establish how the infinite dimensional Boomerang Sampler admits a finite dimensional approximation, rendering it suitable for computer simulation.

Original languageEnglish
Pages (from-to)337-396
Number of pages60
JournalStochastic Processes and their Applications
Volume165
DOIs
Publication statusPublished - 2023

Keywords

  • Hypocoercivity
  • Infinite Dimensional Stochastic Process
  • Piecewise Deterministic Markov Processes
  • Uniform in time approximation

Fingerprint

Dive into the research topics of 'Infinite dimensional Piecewise Deterministic Markov Processes'. Together they form a unique fingerprint.

Cite this