THE ASYMPTOTIC EQUIPARTITION PROPERTY FOR A NONHOMOGENEOUS MARKOV INFORMATION SOURCE

In this paper, we study the asymptotic equipartition property (AEP) fo r a nonhomogeneous Markov information source. We first give a limit th eorem for the averages of the functions of two variables of this infor mation source by using the convergence theorem for the martingale diff erence sequence. As corollaries, we get several limit theorems and a l imit theorem of the relative entropy density, which hold for any nonho mogeneous Markov information source. Then, we get a class of strong la ws of large numbers for nonhomogeneous Markov information sources. Fin ally, we prove the AEP for a class of nonhomogeneous Markov informatio n sources.