Open Access
November, 1993 A New Martingale in Branching Random Walk
A. Joffe
Ann. Appl. Probab. 3(4): 1145-1150 (November, 1993). DOI: 10.1214/aoap/1177005276


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.


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A. Joffe. "A New Martingale in Branching Random Walk." Ann. Appl. Probab. 3 (4) 1145 - 1150, November, 1993.


Published: November, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0784.60081
MathSciNet: MR1241038
Digital Object Identifier: 10.1214/aoap/1177005276

Primary: 60J80
Secondary: 60G42 , 60J15

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

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.3 • No. 4 • November, 1993
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