The exponential family of Markov chains and its information geometry

We introduce a new definiton of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of information geometry is effectively applied to our framework, which enables us to characterize the divergence rate of Markov chain from a differential geometric viewpoint. Keywords— exponential family, Markov chain, Markov process, information geometry