论文标题
马尔可夫链收敛速率的耦合/较小/漂移方法
The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates
论文作者
论文摘要
这篇审查论文提供了马尔可夫连锁店及其收敛速度的介绍，这是一个重要且有趣的数学主题，它也为非常广泛使用的马尔可夫链蒙特卡洛（MCMC）算法提供了重要的应用。我们首先讨论有限状态空间上马尔可夫链的特征值分析。然后，使用耦合结构，我们根据次要条件和漂移条件证明了两个定量界限，并提供了描述性和直观的示例，以展示如何在实践中实现这些定理。本文旨在提供对新马尔可夫连锁研究领域的主题和激增的概述。
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC) algorithm. We first discuss eigenvalue analysis for Markov chains on finite state spaces. Then, using the coupling construction, we prove two quantitative bounds based on minorization condition and drift conditions, and provide descriptive and intuitive examples to showcase how these theorems can be implemented in practice. This paper is meant to provide a general overview of the subject and spark interest in new Markov chain research areas.
