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Birth and Death Process

In: Introduction to Stochastic Processes Using R

Author

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  • Sivaprasad Madhira

    (Savitribai Phule Pune University)

  • Shailaja Deshmukh

    (Savitribai Phule Pune University)

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.

Suggested Citation

  • Sivaprasad Madhira & Shailaja Deshmukh, 2023. "Birth and Death Process," Springer Books, in: Introduction to Stochastic Processes Using R, chapter 0, pages 441-485, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-5601-2_8
    DOI: 10.1007/978-981-99-5601-2_8
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