Some strong deviation theorems for stochastic process indexed by a tree

In this paper we introduce a concept of asymptotic log-likelihood ratio as a measure of deviation of the joint distribution from the product of their margins,we give the generalized strong law of large numbers (strong law expressed by inequalities,i.e. strong deviation theorems) for stochastic process indexed by a tree. as corollaries,we obtain some known results. © 2013 pakistan journal of statistics.