The Annals of Probability
- Ann. Probab.
- Volume 19, Number 3 (1991), 1102-1117.
Weak Convergence to a Markov Chain with an Entrance Boundary: Ancestral Processes in Population Genetics
We derive conditions under which a sequence of processes will converge to a (continuous-time) Markov chain with an entrance boundary. Our main application of this result is in proving weak convergence of the so-called population ancestral processes, associated with a wide class of exchangeable reproductive models, to a particular death process with an entrance boundary at infinity. This settles a conjecture of Kingman. We also prove weak convergence of the absorption times of many neutral genetics models to that of the Wright-Fisher diffusion, and convergence of population line-of-descent processes to another death process.
Ann. Probab., Volume 19, Number 3 (1991), 1102-1117.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 60F99: None of the above, but in this section 60J27: Continuous-time Markov processes on discrete state spaces
Donnelly, Peter. Weak Convergence to a Markov Chain with an Entrance Boundary: Ancestral Processes in Population Genetics. Ann. Probab. 19 (1991), no. 3, 1102--1117. doi:10.1214/aop/1176990336. https://projecteuclid.org/euclid.aop/1176990336