Maximum Entropy for Determining the Transition Probability Matrix of a Markov Chain with a Specified Stationary Distribution

Abstract

In this paper, we try to find the unknown transition probability matrix of a Markov chain that has a specific stationary distribution. Numerous Markov chains can be found with this property, but among these Markov chains, we want to choose one with the highest entropy rate. In this case, we claim that the Markov chain where the rows of its transition probability matrix are of identical distribution to the stationary distribution, has the maximum entropy rate.