@article{ECP1054,
author = {Jeffrey Rosenthal},
title = {Quantitative Convergence Rates of Markov Chains: A Simple Account},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {7},
year = {2002},
keywords = {Markov chain, convergence rate, mixing time, drift condition, minorisation condition, total variation distance.},
abstract = {We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition probabilities. The result is a simplified and improved version of the result in Rosenthal (1995), which also takes into account the $epsilon$-improvement of Roberts and Tweedie (1999), and which follows as a special case of the more complicated time-inhomogeneous results of Douc et al. (2002). However, the proof we present is very short and simple; and we feel that it is worthwhile to boil the proof down to its essence. This paper is purely expository; no new results are presented.},
pages = {no. 13, 123-128},
issn = {1083-589X},
doi = {10.1214/ECP.v7-1054},
url = {http://ecp.ejpecp.org/article/view/1054}}