On Risk Rates and Large Deviations in Finite Markov Chain Experiments
Peter Scheffel, Heinrich v. Weizsacker · 1997
The observation of an ergodic Markov chain asymptotically allows perfect identification of the transition matrix. In this paper we determine the rate of the information contained in the first n observations, provided the unknown transition matrix belongs to a known finite set. As an essential tool we prove new refinements of the large deviation theory of the empirical pair measure of finite Markov chains.