1 results
Asymptotic persistence time formulae for multitype birth–death processes
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 60 / Issue 3 / September 2023
- Published online by Cambridge University Press:
- 21 March 2023, pp. 895-920
- Print publication:
- September 2023
-
- Article
-
- You have access
- HTML
- Export citation
-
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
$ {\mathbb Z}_+^k$; we allow the possibility that individuals’ lifetimes may follow more general distributions than the exponential distribution.
