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Birth–Death Processes with Two-Type Catastrophes

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  • Junping Li

    (Guangdong University of Science & Technology, Dongguan 523083, China
    School of Mathematics and Statistics, Central South University, Changsha 410083, China)

Abstract

This paper concentrates on the general birth–death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth–death processes with two-type catastrophes is successfully expressed with the Laplace transform of transition probability function of the birth–death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

Suggested Citation

  • Junping Li, 2024. "Birth–Death Processes with Two-Type Catastrophes," Mathematics, MDPI, vol. 12(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1468-:d:1391158
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    References listed on IDEAS

    as
    1. Economou, Antonis & Fakinos, Demetrios, 2003. "A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes," European Journal of Operational Research, Elsevier, vol. 149(3), pages 625-640, September.
    2. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    3. Di Crescenzo, A. & Giorno, V. & Nobile, A.G. & Ricciardi, L.M., 2008. "A note on birth-death processes with catastrophes," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2248-2257, October.
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