Piecewise linear process with renewal starting points
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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. © 2017 Elsevier B.V.
Continuous-time homogeneous Markov chain , First passage time , Piecewise linear process , Renewal process