Piecewise linear process with renewal starting points

Nikita Ratanov ()

Statistics & Probability Letters, 2017, vol. 131, issue C, 78-86

Abstract: 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.

Keywords: Continuous-time homogeneous Markov chain; Piecewise linear process; Renewal process; First passage time (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.08.010

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