The Annals of Applied Probability

A New Martingale in Branching Random Walk

A. Joffe

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 4 (1993), 1145-1150.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005276

Digital Object Identifier
doi:10.1214/aoap/1177005276

Mathematical Reviews number (MathSciNet)
MR1241038

Zentralblatt MATH identifier
0784.60081

JSTOR
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G42: Martingales with discrete parameter 60J15

Keywords
Spatial growth in branching random walk Banach space valued martingales genealogy of Galton-Watson tree

Citation

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


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