论文标题
分段确定的马尔可夫进程蒙特卡洛方法的子几何脑质量
Subgeometric hypocoercivity for piecewise-deterministic Markov process Monte Carlo methods
论文作者
论文摘要
我们扩展了[Andrieu等人在[Andrieu Et。 al。 （2018）]对重尾目标分布，该分布表现出与平衡的收敛速率。我们利用了[Grothaus and Wang（2019）]的工作中发展的薄弱的庞加莱不平等现象，我们适应了感兴趣的PDMP。在我们的方式上，我们报告了在很大程度上独立于潜在的无关方法，以明确地解决兰格文扩散的泊松方程及其第一个和第二个衍生物，以控制在应用低调结果时产生的各种术语。
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 Poincaré 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.
