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Infinite dimensional Piecewise Deterministic Markov Processes

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  • Dobson, Paul
  • Bierkens, Joris

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.

Suggested Citation

  • Dobson, Paul & Bierkens, Joris, 2023. "Infinite dimensional Piecewise Deterministic Markov Processes," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 337-396.
    • Handle: RePEc:eee:spapps:v:165:y:2023:i:c:p:337-396
    DOI: 10.1016/j.spa.2023.08.010
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    References listed on IDEAS

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    1. Alexandre Bouchard-Côté & Sebastian J. Vollmer & Arnaud Doucet, 2018. "The Bouncy Particle Sampler: A Nonreversible Rejection-Free Markov Chain Monte Carlo Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 855-867, April.
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