139 citations · 616 across the 32 of their papers we have counts for
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Infinite Dimensional Piecewise Deterministic Markov Processes
Paul Dobson, Joris Bierkens
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 Sa…
Approximations of Piecewise Deterministic Markov Processes and their convergence properties
Andrea Bertazzi, Joris Bierkens, Paul Dobson
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling…
Large deviations for the empirical measure of the zig-zag process
Joris Bierkens, Pierre Nyquist, Mikola C. Schlottke
The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability den…
Spectral analysis of the zigzag process
Joris Bierkens, Sjoerd M. Verduyn Lunel
The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the -spectrum for the generator of the one-dimens…
Simulation of elliptic and hypo-elliptic conditional diffusions
Joris Bierkens, Frank van der Meulen, Moritz Schauer
Suppose is a multidimensional diffusion process. Assume that at time zero the state of is fully observed, but at time only linear combinations of its components are o…
High-dimensional scaling limits of piecewise deterministic sampling algorithms
Joris Bierkens, Kengo Kamatani, Gareth O. Roberts
Piecewise deterministic Markov processes are an important new tool in the design of Markov Chain Monte Carlo algorithms. Two examples of fundamental importance are the Bouncy Parti…