Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains
Probability
2020-12-29 v1
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.
Keywords
Cite
@article{arxiv.2012.13895,
title = {Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains},
author = {Lu-Jing Huang and Yong-Hua Mao},
journal= {arXiv preprint arXiv:2012.13895},
year = {2020}
}