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

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 nth 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 L2 under weak assumptions on the displacement of the particles and strong assumptions on the branching.

Citation

Download Citation

A. Joffe. "A New Martingale in Branching Random Walk." Ann. Appl. Probab. 3 (4) 1145 - 1150, November, 1993. https://doi.org/10.1214/aoap/1177005276

Information

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

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

Subjects:
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
Back to Top