On the hypocoercivity of some PDMP-Monte Carlo algorithms

With Christophe Andrieu, University of Bristol

On the hypocoercivity of some PDMP-Monte Carlo algorithms

Monte Carlo methods based on Piecewise Deterministic Markov Processes (PDMP) have recently received some attention. In this talk we discuss (exponential) convergence to equilibrium for a broad sub-class of PDMP -MC, covering Randomized Hamiltonian Monte Carlo, the Zig-Zag process and the Bouncy Particle Sampler as particular cases, establishing hypocoercivity under fairly weak conditions and explicit bounds on the spectral gap in terms of the parameters of the dynamics. This allows us, for example, to discuss dependence of this gap on the dimension of the problem for some classes of target distributions.


(joint work with Alain Durmus, Nikolas Nüsken, Julien Roussel)

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