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arXiv · 2008.10675

The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates

Yu Hang Jiang·Tong Liu·Zhiya Lou·Jeffrey S. Rosenthal·Shanshan Shangguan·Fei Wang·Zixuan Wu
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Abstract

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.

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Yu Hang Jiang, Tong Liu, Zhiya Lou, Jeffrey S. Rosenthal, Shanshan Shangguan, Fei Wang, Zixuan Wu. 2021-09-02. The Coupling/Minorization/Drift Approach to Markov Chain Convergence Rates. https://doi.org/10.1090/noti2253

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