Birth and Death Process

Sivaprasad Madhira and Shailaja Deshmukh ()
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Sivaprasad Madhira: Savitribai Phule Pune University
Shailaja Deshmukh: Savitribai Phule Pune University

Chapter Chapter 8 in Introduction to Stochastic Processes Using R, 2023, pp 441-485 from Springer

Abstract: Abstract A birth-death process is a generalization of the Poisson process. Being a continuous time Markov chain, the sojourn times in states of a birth-death process are exponential, but the rates are state-dependent. In Sect. 2, a pure birth process is defined and a linear birth process is studied in detail. Sections 3 and 4 are devoted to a death process and a birth-death process, respectively. Section 5 is concerned with a linear birth-death process (linear growth model) and its variations that incorporate immigration/emigration components. In Sect. 6, the long-run distribution of the birth-death processes is discussed. Section 7 presents R codes for realizations of these processes.

Date: 2023
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DOI: 10.1007/978-981-99-5601-2_8

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