  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.
