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Piecewise linear process with renewal starting points

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  • Ratanov, Nikita

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.

Suggested Citation

  • Ratanov, Nikita, 2017. "Piecewise linear process with renewal starting points," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 78-86.
    • Handle: RePEc:eee:stapro:v:131:y:2017:i:c:p:78-86
    DOI: 10.1016/j.spl.2017.08.010
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    References listed on IDEAS

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    1. Ratanov, Nikita, 2014. "On piecewise linear processes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 60-67.
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    Cited by:

    1. Nikita Ratanov, 2020. "Kac–Lévy Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 239-267, March.

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