Before revision: We study an extension of optimal transport techniques to stationary Markov chains from a computational perspective. In this context, naively applying optimal transport to the stationary distributions of the Markov chainsof interest would not capture the Markovian dynamics. Instead, we study a new problem, called the optimal transition coupling problem, in which the optimal transport problem is constrained to the set of stationary Markovian couplings satisfying a certain transition matrix condition.
After revision: We study an extension of optimal transport techniques to stationary Markov chains . Solutions of the optimal transition coupling problem, in which the optimal transport problem is constrained to the set of stationary Markovian couplings satisfying a certain transition matrix condition.