We extend the hypocoercivity framework for piecewise-deterministic Markov process (PDMP) Monte Carlo established in [Andrieu et. al. (2018)] to heavy-tailed target distributions, which exhibit subgeometric rates of convergence to equilibrium. We make use of weak Poincar\'e inequalities, as developed in the work of [Grothaus and Wang (2019)], the ideas of which we adapt to the PDMPs of interest. On the way we report largely potential-independent approaches to bounding explicitly solutions of the Poisson equation of the Langevin diffusion and its first and second derivatives, required here to control various terms arising in the application of the hypocoercivity result.
翻译:我们把在[Andrieu等人(2018年) 建立的Papidocol(PDMP)Monte Carlo(PDMP)程序(PDMP)的低胁迫性框架扩大到重尾目标分布,这些分布显示出与均衡相趋同的亚几何率。我们利用了[Grothaus和Wang(2019年) 工作中形成的薄弱的Poincar(Pincar)不平等,我们对这些不平等的想法进行了调整以适应人们感兴趣的PDMP。我们报告的方式是,我们报告对Langevin扩散的Poisson等式及其第一和第二衍生物的明确解决方案进行约束的潜在独立方法,这里需要控制在应用低连接结果时产生的各种条件。