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2002 Quantitative Convergence Rates of Markov Chains: A Simple Account
Jeffrey Rosenthal
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Electron. Commun. Probab. 7: 123-128 (2002). DOI: 10.1214/ECP.v7-1054


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.


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Jeffrey Rosenthal. "Quantitative Convergence Rates of Markov Chains: A Simple Account." Electron. Commun. Probab. 7 123 - 128, 2002.


Accepted: 10 May 2002; Published: 2002
First available in Project Euclid: 16 May 2016

zbMATH: 1013.60053
MathSciNet: MR1917546
Digital Object Identifier: 10.1214/ECP.v7-1054

Primary: 60J05
Secondary: 62M05


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