Asymptotic persistence time formulae for multitype birth–death processes

Frank G. Ball, Damian Clancy

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We consider a class of processes describing a population consisting of k types of individuals. The process is almost surely absorbed at the origin within finite time, and we study the expected time taken for such extinction to occur. We derive simple and precise asymptotic estimates for this expected persistence time, starting either from a single individual or from a quasi-equilibrium state, in the limit as a system size parameter N tends to infinity. Our process need not be a Markov process on Zk+ ; we allow the possibility that individuals’ lifetimes may follow more general distributions than the exponential distribution.
Original languageEnglish
JournalJournal of Applied Probability
Early online date21 Mar 2023
Publication statusE-pub ahead of print - 21 Mar 2023


  • Large deviations
  • population processes
  • stochastic epidemic models

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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