Asymptotic persistence time formulae for multitype birth-death processes

Ball, Frank G; Clancy, Damian

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: Sep 22, 2023
• Journal: Journal of Applied Probability
• Print ISSN: 0021-9002
• Electronic ISSN: 1475-6072
• Publisher: Applied Probability Trust
• 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.