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On explicit \(L^2\)-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms. (English) Zbl 1490.60218

The authors establish \(L^2\)-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process and the bouncy particle sampler.
The analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard \(L^2\) energy estimate.
Explicit convergence rate estimates are provided, which are more quantitative than the existing results.

MSC:

60J22 Computational methods in Markov chains
60J25 Continuous-time Markov processes on general state spaces
65C40 Numerical analysis or methods applied to Markov chains
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