ASYMPTOTIC PERSISTENCE TIME FORMULAE FOR MULTI- TYPE 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. (in press). ASYMPTOTIC PERSISTENCE TIME FORMULAE FOR MULTI- TYPE BIRTH-DEATH PROCESSES. Journal of Applied Probability,

Journal Article Type	Article
Acceptance Date	Aug 24, 2022
Deposit Date	Sep 28, 2022
Print ISSN	0021-9002
Electronic ISSN	1475-6072
Publisher	Applied Probability Trust
Peer Reviewed	Peer Reviewed
Keywords	Large deviations; population processes; stochastic epidemic models
Public URL	https://nottingham-repository.worktribe.com/output/11750259