Piecewise linear process with renewal starting points

This paper concerns a Markovian piecewise linear process, based on a continuous-time Markov chain with a finite state space. The process describes the movement of a particle that takes a new linear trend starting from a new random point (with state-dependent distribution) after each trend switch. The distribution of particle's position is derived in a closed form. In some special cases the distributions of the level passage times are provided explicitly.