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 Electronic Communications in Probability > Vol. 7 (2002) > Paper 13 open journal systems 


Quantitative Convergence Rates of Markov Chains: A Simple Account

Jeffrey S. Rosenthal, University of Toronto


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.


Full text: PDF

Pages: 123-128

Published on: May 10, 2002
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Electronic Communications in Probability. ISSN: 1083-589X