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 language | English |
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Pages (from-to) | 337-396 |
Number of pages | 60 |
Journal | Stochastic Processes and their Applications |
Volume | 165 |
Early online date | 9 Sept 2023 |
DOIs | |
Publication status | Published - Nov 2023 |
Keywords
- Hypocoercivity
- Infinite Dimensional Stochastic Process
- Piecewise Deterministic Markov Processes
- Uniform in time approximation
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics