The asymptotic equipartition property for countable m th-order nonhomogeneous Markov chains

In this paper,we first establish a strong law of large numbers for averages of the functions of m+1 variables of countable mth-order nonhomogeneous markov chains. as corollaries,we obtain the asymptotic equipartition property (aep) for countable mth-order nonhomogeneous markov chains which generalize the results for finite case. we also generalize the results for countable first-order nonhomogeneous markov chains in a sense. by the way,we give an extension of a strong law of large numbers for functional of countable nonhomogeneous markov chains at the same time. © 2013 pakistan journal of statistics.