Math @ Duke
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Publications [#361285] of Jianfeng Lu
Papers Published
- Lu, J; Wang, L, On explicit $L^2$-convergence rate estimate for piecewise deterministic
Markov processes in MCMC algorithms,
Ann. Appl. Probab. 32(2): 1333-1361 (April 2022)
(July, 2020)
(last updated on 2024/09/17)
Abstract: 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
Poincar\'{e}-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 results.
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