A Class of Random Approximation Theoremsfor Random Sums of Arbitrary Stochastic Sequence

In this paper, the notion of limit random logarithmic likelihood ratio of stochastic sequence, as a measure of dissimilarity between the joint distribution on measure \pr and the two-order Markov distribution on measure \qr, is introduced. A class of random approximation theorems for random sum of arbitrary stochastic dominated sequence on random selection system has been obtained by using the tools of generating function and the tailed-probability generating function.