  We study the local limit distribution of the number of occurrences of a
symbol in words of length $n$ generated at random in a regular language
according to a rational stochastic model. We present an analysis of the main
local limits when the finite state automaton defining the stochastic model
consists of two primitive components. The limit distributions depend on several
parameters and conditions, such as the main constants of mean value and
variance of our statistics associated with the two components, and the
existence of communications from the first to the second component. The
convergence rate of these results is always of order $O(n^{-1/2})$. We also
prove an analogous $O(n^{-1/2})$ convergence rate to a Gaussian density of the
same statistic whenever the stochastic models only consists of one (primitive)
component.
