Abstract: Let XX... be a sequence of strictly stationary discrete random variables with probability generating function (t) and let (t) n 1=1 X1 = be the empirical probability generating function of the first n random variables. A strong law of large numbers and the weak convergence of 1/2-) to a Gaussian process are discussed. These n n results are extended to a sequence of stationary multivariate discrete random variables and to integer valued stationary stochastic processes. Applications to the statistical analysis of discrete data are discussed Ver menos