On Time-Changed Linear Birth–Death–Immigration Process

K. K. Kataria () and P. Vishwakarma ()
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K. K. Kataria: Indian Institute of Technology Bhilai
P. Vishwakarma: Indian Institute of Technology Bhilai

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-24

Abstract: Abstract We introduce and study a time-changed variant of the linear birth–death process under an immigration effect. Here, the time is changed via an inverse stable subordinator. It is shown that the state probabilities of this immigration model are governed by a system of fractional differential equations. We obtain the explicit expressions for its transient probabilities in three different cases of its birth, death and immigration rates. Also, some particular cases of this process are studied in detail.

Keywords: Extinction probability; Time-fractional linear birth–death–immigration process; Caputo fractional derivative; Inverse stable subordinator; 60J27; 60J80 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01387-5

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