On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms

@article{Lu2022OnEL,
  title={On explicit L2-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms},
  author={Jianfeng Lu and Lihan Wang},
  journal={The Annals of Applied Probability},
  year={2022}
}
. We 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. Our 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. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing… 

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