论文标题
用状态依赖性和非本地碰撞的抑制哈密顿动力学的指数千古性
Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions
论文作者
论文摘要
在本文中，我们研究了沃斯坦型型距离中的指数成分性，用于阻尼的汉密尔顿动态，具有州依赖性和非本地碰撞，这确实是分段确定性马尔可夫过程的特殊情况，而在包括随机算法在内的许多建模情况下非常流行。这项工作中采用的方法是基于精制基本耦合和非本地运算符的精制反射耦合的组合。从某种意义上说，本文在本文中产生的主要结果是在\ cite {bw2022}中延续了对应于随机噪声的随机汉密尔顿系统的指数级数，并补充了\ cite {ba}的补充，{ba}对安德森持续跳高函数的指数性呈元素的良好性效果。
In this paper, we investigate the exponential ergodicity in a Wasserstein-type distance for a damping Hamiltonian dynamics with state-dependent and non-local collisions, which indeed is a special case of piecewise deterministic Markov processes while is very popular in numerous modelling situations including stochastic algorithms. The approach adopted in this work is based on a combination of the refined basic coupling and the refined reflection coupling for non-local operators. In a certain sense, the main result developed in the present paper is a continuation of the counterpart in \cite{BW2022} on exponential ergodicity of stochastic Hamiltonian systems with Lévy noises and a complement of \cite{BA} upon exponential ergodicity for Andersen dynamics with constant jump rate functions.
