  Let $I$ be a finite alphabet and $\aS\subset I$ be a nonempty strict subset.
The sequences in $I^\ZZ$ are organized into connected regions which always
start with a symbol in $\aS$. The regions are labelled by types $C(s)$, thus a
region starting at $s'\in C(s)$ has the same type as one starting at $s$. Let
$(\aP_s: s\in \aS)$ be a family of distributions on $I^\NN$ where each $\aP_s$
charges sequences starting with the symbol $s$. We can define a natural
distribution $\PP$ on $I^\NN$, that counts the number of visits to the states
from $\aP_s$, properly weighted. A dynamics of interest is such that at the
first occurrence of $s'\in \aS\setminus C(s)$ the law regenerates with
distribution $\aP_{s'}$. In this case we are able to find simple conditions for
$\PP$ to be stationary. In addition, we study the following more complex model:
once a symbol $s'\in \aS\setminus C(s)$ has been encountered, there is a
decision to be made, either a new region of type $C(s')$ governed by $\aP_{s'}$
starts or the region continues to be a $C(s)$ region. This decision is modeled
as random and depends on $s'$. In this setting a similar distribution to $\PP$
can be constructed and the conditions for stationarity are supplied. These
models are inspired by genomic sequences where $I$ is the set of codons, the
classes $(C(s): s\in \aS)$ group codons defining similar genomic classes, e.g.
in bacteria there are two classes corresponding to the start and stop codons,
and the random decision to continue a region or to begin a new region of a
different class reflects the well-known fact that not every appearance of a
start codon marks the beginning of a new coding region.
