  The aim of this work is to provide a rigorous mathematical analysis of a
stochastic concatenation model presented by Sobottka and Hart (2011) which
allows approximation of the first-order stochastic structure in bacterial DNA
by means of a stationary Markov chain. Two probabilistic constructions that
rigorously formalize the model are presented. Necessary and sufficient
conditions for a Markov chain to be generated by the model are given, as well
as the theoretical background needed for designing new algorithms for
statistical analyses of real bacterial genomes. It is shown that the model
encompasses the Markov chains satisfying intra-strand parity, a property
observed in most DNA sequences.
