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Asymptotic persistence time formulae for multitype birth-death processes

Ball, Frank G; Clancy, Damian

Authors

FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability

Damian Clancy



Abstract

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 Z k + ; we allow the possibility that individuals' lifetimes may follow more general distributions than the exponential distribution.

Citation

Ball, F. G., & Clancy, D. (2023). Asymptotic persistence time formulae for multitype birth-death processes. Journal of Applied Probability, 60(3), 895-920. https://doi.org/10.1017/jpr.2022.102

Journal Article Type Article
Acceptance Date Aug 24, 2022
Online Publication Date Mar 21, 2023
Publication Date Mar 21, 2023
Deposit Date Sep 28, 2022
Publicly Available Date Mar 29, 2024
Journal Journal of Applied Probability
Print ISSN 0021-9002
Electronic ISSN 1475-6072
Peer Reviewed Peer Reviewed
Volume 60
Issue 3
Pages 895-920
DOI https://doi.org/10.1017/jpr.2022.102
Keywords Large deviations; population processes; stochastic epidemic models
Public URL https://nottingham-repository.worktribe.com/output/11750259
Publisher URL https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/asymptotic-persistence-time-formulae-for-multitype-birthdeath-processes/4F78DE9122149576DF56D44CA65F276B
Additional Information This article has been published in a revised form in Journal of Applied Probability https://doi.org/10.1017/jpr.2022.102. This version is published under a Creative Commons CC-BY-NC-ND licence. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © copyright holder.

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