Exponential ergodicity for damping Hamiltonian dynamics with state-dependent and non-local collisions

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2022-04-04 DOI:10.3150/22-bej1548

J. Bao, Jian Wang

引用次数: 0

Abstract

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 L\'evy noises and a complement of \cite{BA} upon exponential ergodicity for Andersen dynamics with constant jump rate functions.

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具有状态相关和非局部碰撞的阻尼哈密顿动力学的指数遍历性

在本文中，我们研究了具有状态相关和非局部碰撞的阻尼哈密顿动力学在Wasserstein型距离内的指数遍历性，这确实是分段确定性马尔可夫过程的一个特例，但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非局部算子的精细基本耦合和精细反射耦合的组合。在某种意义上，本文发展的主要结果是关于具有L’evy噪声的随机Hamilton系统的指数遍历性的对应项的延续，以及关于具有常跳率函数的Andersen动力学的指数遍历的补充。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.