Infinite dimensional Piecewise Deterministic Markov Processes
Paul Dobson (Heriot-Watt University, TU Delft - Electrical Engineering, Mathematics and Computer Science)
Joris Bierkens (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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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.
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