Electronic Communications in Probability

A strong law of large numbers for branching processes: almost sure spine events

Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 28, 6 pp.

Dates
Accepted: 8 May 2014
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465316730

Digital Object Identifier
doi:10.1214/ECP.v19-2641

Mathematical Reviews number (MathSciNet)
MR3208326

Zentralblatt MATH identifier
1312.60022

Rights
• Hardy, Robert; Harris, Simon C. A spine approach to branching diffusions with applications to $\scr L^ p$-convergence of martingales. SÄ‚Å minaire de ProbabilitÄ‚Å s XLII, 281–330, Lecture Notes in Math., 1979, Springer, Berlin, 2009.