Electronic Communications in Probability

Quantitative Convergence Rates of Markov Chains: A Simple Account

Jeffrey Rosenthal

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463434780

Digital Object Identifier
doi:10.1214/ECP.v7-1054

Mathematical Reviews number (MathSciNet)
MR1917546

Zentralblatt MATH identifier
1013.60053

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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