Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains

2020/12/27 by Lu‐Jing Huang, Huang, Lu-Jing, Yong-Hua Mao +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2012.13895

openalex publication_date 2020/12/27 · openalex created_date 2021/01/05 · openalex updated_date 2026/07/28

Abstract

The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov chains on general state space. The variational formulas provide many applications, extending the classical Peskun's comparison theorem to non-reversible Markov chains, and obtaining several comparison theorems between Markov chains with various perturbations.

Citations

• Variational principles for the exit time of non-symmetric diffusions

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