ON EXPLICIT L2-CONVERGENCE RATE ESTIMATE FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES IN MCMC ALGORITHMS

• 成果类型: Article
• 署名作者: Lu, Jianfeng; Wang, Lihan
• 署名单位: Duke University; Duke University; Duke University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1710
• 发表日期: 2022
• 页码: 1333-1361
• 关键词: kinetic-equations; monte-carlo; hypocoercivity; ergodicity

摘要

We establish L-2-exponential convergence rate for three popular piece-wise 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 Poincare-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.