Intersections of the interval and reflections for a semi-Markov walk with linear drift

Abstract

Several two-boundary problems are solved for a semi-Markov random walk with a linear drift. The Laplace transforms of the joint distribution of the number of upward and downward intersection of the interval by the process. We also find the Laplace transforms of the boundary functionals of the processes reflected at their boundaries. The results obtained are applied for a special case when the jumps of the process are exponentially distributed.Key words. The semi-Markov walk with a linear drift; exit from an interval; upward and downward intersection of the interval; reflected processes.