Frequency of symbol occurrences in bicomponent stochastic models

We give asymptotic estimates of the frequency of occurrences of a symbol in a random word generated by any bicomponent stochastic model. More precisely, we consider the random variable Yn representing the number of occurrences of a given symbol in a word of length n generated at random; the stochastic model is defined by a rational formal series r having a linear representation with two primitive components. This model includes the case when r is the product or the sum of two primitive rational formal series. We obtain asymptotic evaluations for the mean value and the variance of Yn and its limit distribution. © 2004 Elsevier B.V. All rights reserved.