Variational principles for asymptotic variance of general Markov processes

2021/06/01 by Lu‐Jing Huang, Huang, Lu-Jing, Yong-Hua Mao +3
Mathematics · #60J25 #60J46 #60J60 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2106.00324

openalex publication_date 2021/06/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and non-reversible diffusion processes.

Related

• Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains
• Asymptotic variance of stationary reversible and normal Markov processes
• Reversible Markov chains: variational representations and ordering
• Variational principles for the exit time of non-symmetric diffusions
• CLTs and asymptotic variance of time-sampled Markov chains