Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 28, 6 pp.
A strong law of large numbers for branching processes: almost sure spine events
We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the spine entails the almost sure convergence of a certain sum over particles in the population.
Electron. Commun. Probab., Volume 19 (2014), paper no. 28, 6 pp.
Accepted: 8 May 2014
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
Harris, Simon; Roberts, Matthew. A strong law of large numbers for branching processes: almost sure spine events. Electron. Commun. Probab. 19 (2014), paper no. 28, 6 pp. doi:10.1214/ECP.v19-2641. https://projecteuclid.org/euclid.ecp/1465316730