Characterization of Ergodic Hidden Markov Sources
An algebraic criterion for the ergodicity of discrete random sources is presented. For finite-dimensional sources, which contain hidden Markov sources as a subclass, the criterion can be effectively computed. This result is obtained on the background of a novel, elementary theory of discrete random sources, which is based on linear spaces spanned by word functions, and linear operators; on these spaces. An outline of basic elements of this theory is provided.
ergodic random source asymptotic mean stationarity dimension entropy evolution operator hidden markov model linearly dependent process markov chain observable operator model stable state generating function stationary