Generalized integrated telegraph processes and the distribution of related stopping times

Abstract

Let {X(t),V(t),t≥ 0} be a telegraph process, withV(0+) = 1. The distribution ofX(t) is derived for the general case of an alternating renewal process, describing the length of time a particle is moving to the right or to the left. The distributions of the first-crossing times of given levelsaand −aare studied for M/G and for G/M processes.