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.
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