A class of strong laws for functionals of countable nonhomogeneous Markov chains

In this paper, we use an analytic approach to study the limit properties of {inn(Xn)}, the functional of a countable nonhomogeneous Markov chain {Xn}. A class of strong laws of large numbers for these processes, which are different from the usual ones, are obtained. In the theorems of this paper, the expectation E(fn(Xn)) in the usual strong laws of large numbers is replaced by the conditional expectation E(fn(Xn(Xn-1)). Some classical strong laws of large numbers for sequences of independent random variables are implied by the results of this paper.