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Quantitative Convergence Rates of Markov Chains: A Simple Account


 
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1. Title Title of document Quantitative Convergence Rates of Markov Chains: A Simple Account
 
2. Creator Author's name, affiliation, country Jeffrey S. Rosenthal; University of Toronto
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Markov chain, convergence rate, mixing time, drift condition, minorisation condition, total variation distance.
 
3. Subject Subject classification Primary 60J05; secondary 62M05.
 
4. Description 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.
 
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7. Date (YYYY-MM-DD) 2002-05-10
 
8. Type Status & genre Peer-reviewed Article
 
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9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1054
 
10. Identifier Digital Object Identifier 10.1214/ECP.v7-1054
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 7
 
12. Language English=en en
 
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