Potential measures of one-sided Markov additive processes with reflecting and terminating barriers

Abstract

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.