The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 3, Number 4 (1993), 1145-1150.
A New Martingale in Branching Random Walk
Martingale methods have played an important role in the theory of Galton-Watson processes and branching random walks. The (random) Fourier transform of the position of the particles in the $n$th generation, normalized by its mean, is a martingale. Under second moments assumptions on the branching this has been very useful to study the asymptotics of the branching random walk. Using a different normalization, we obtain a new martingale which is in $L^2$ under weak assumptions on the displacement of the particles and strong assumptions on the branching.
Ann. Appl. Probab., Volume 3, Number 4 (1993), 1145-1150.
First available in Project Euclid: 19 April 2007
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.)
Secondary: 60G42: Martingales with discrete parameter 60J15
Joffe, A. A New Martingale in Branching Random Walk. Ann. Appl. Probab. 3 (1993), no. 4, 1145--1150. doi:10.1214/aoap/1177005276. https://projecteuclid.org/euclid.aoap/1177005276