Bounds on Expected Coupling Times in a Markov Chain
In the author's paper “Coupling and Mixing Times in Markov Chains” (Res. Lett. Inf. Math. Sci, 11, 1–22, 2007) it was shown that it is very difficult to find explicit expressions for the expected time to coupling in a general Markov chain. In this paper simple upper and lower bounds are given for the expected time to coupling in a discrete time finite Markov chain. Extensions to the bounds under additional restrictive conditions are also given with detailed comparisons provided for two and three state chains.
KeywordsMarkov Chain Transition Matrix Independent Trial Coupling Time Stationary Probability Vector
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