In the author’s paper “Coupling and Mixing Times in Markov Chains” (RLIMS, 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.
Hunter, J.J. (2008), Bounds on expected coupling times in Markov chains, Research Letters in the Information and Mathematical Sciences, 12, 1-23