In this work we study some probabilistic models for the random generation of words over a given alphabet
used in the literature in connection with pattern statistics.
Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given position
only depends on a finite number of previous occurrences) and the stochastic models that
can generate a word of given length from a regular language under uniform distribution.
We present some results that show the differences between these two stochastic models and their
relationship with the rational probabilistic measures.