A Class Of Strong Deviation Theorems For Partial Sums Of Random Variables And Some Limit Theorems On Two Classes Of Trees

In this paper, the notion of likelihood ratio, as a measure of deviation between a sequence of the arbitrary random variables and a sequence of independent random variables with different distributions, is introduced. A class of strong deviation theorems represented by inequalities are given on a subset of the sample space by constructing a negative supermartingale and using martingale convergence theorem. In the third section, the asymptotic equipartition property(AEP) of second order markov chain field on a class of tree is studied by using the analytic approach. A net is constructed on a product space, then some strong laws of large numbers of second order markov chain field are proved by using the differentiation of measure on a net. Furthermore, Shannon-Mcmillan theorem is extended to the case of second order markov chain field. In the fourth section, furthermore, we study the markov approximation of the random fields on a homogeneous tree.