  For hidden Markov models one of the most popular estimates of the hidden
chain is the Viterbi path -- the path maximising the posterior probability. We
consider a more general setting, called the pairwise Markov model, where the
joint process consisting of finite-state hidden regime and observation process
is assumed to be a Markov chain. We prove that under some conditions it is
possible to extend the Viterbi path to infinity for almost every observation
sequence which in turn enables to define an infinite Viterbi decoding of the
observation process, called the Viterbi process. This is done by constructing a
block of observations, called a barrier, which ensures that the Viterbi path
goes trough a given state whenever this block occurs in the observation
sequence.
