Some Shannon-McMillan Theorems for Nonhomogeneous Markov chains Indexed by a Tree on Generalized Gambling Systems (pp.3-17)

摘要

In this paper, a class of generalized Shannon-McMillan theorems for the nonhomogeneousMarkov chains field on an infinite tree with respect to the generalized randomselection system are discussed by constructing a nonnegative martingale. As corollaries,some Shannon-Mcmillan theorems for the homogeneous Markov chains field on aninfinite tree and the nonhomogeneous Markov chain are obtained. Some results whichhave been obtained are extended.