Electronic Communications in Probability

Quantitative Convergence Rates of Markov Chains: A Simple Account

Jeffrey Rosenthal

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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.

Article information

Electron. Commun. Probab., Volume 7 (2002), paper no. 13, 123-128.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M05: Markov processes: estimation

Markov chain convergence rate mixing time drift condition minorisation condition total variation distance

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Rosenthal, Jeffrey. Quantitative Convergence Rates of Markov Chains: A Simple Account. Electron. Commun. Probab. 7 (2002), paper no. 13, 123--128. doi:10.1214/ECP.v7-1054. https://projecteuclid.org/euclid.ecp/1463434780

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