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Article

Birth–Death Processes with Two-Type Catastrophes

1
Guangdong University of Science & Technology, Dongguan 523083, China
2
School of Mathematics and Statistics, Central South University, Changsha 410083, China
Mathematics 2024, 12(10), 1468; https://doi.org/10.3390/math12101468
Submission received: 4 April 2024 / Revised: 23 April 2024 / Accepted: 7 May 2024 / Published: 9 May 2024
(This article belongs to the Special Issue Probability, Statistics and Random Processes)

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.
Keywords: birth–death process; catastrophe; Laplace transform; probability density function birth–death process; catastrophe; Laplace transform; probability density function

Share and Cite

MDPI and ACS Style

Li, J. Birth–Death Processes with Two-Type Catastrophes. Mathematics 2024, 12, 1468. https://doi.org/10.3390/math12101468

AMA Style

Li J. Birth–Death Processes with Two-Type Catastrophes. Mathematics. 2024; 12(10):1468. https://doi.org/10.3390/math12101468

Chicago/Turabian Style

Li, Junping. 2024. "Birth–Death Processes with Two-Type Catastrophes" Mathematics 12, no. 10: 1468. https://doi.org/10.3390/math12101468

APA Style

Li, J. (2024). Birth–Death Processes with Two-Type Catastrophes. Mathematics, 12(10), 1468. https://doi.org/10.3390/math12101468

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