  Consider a one-sided Markov additive process with an upper and a lower
barrier, where each can be either reflecting or terminating. For both defective
and non-defective processes and all possible scenarios we identify the
corresponding potential measures, which generalizes a number of results for
one-sided Levy processes. The resulting rather neat formulas have various
applications, and in particular they lead to quasi-stationary distributions of
the corresponding processes.
