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A prediction problem of the branching random walk

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

P. Révész
P. Révész*
Affiliation:
Technische Universität Wien, Institut für Statistik und Wahrscheinlichkeitstheorie, Wiedner Hauptstasse 8-10/107, Wien, A-1040 Austria. Email address: pal.revesz@ci.tuwien.ac.at
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Abstract

The location of the ‘favourite’ point at time T (T = 1, 2,…) of a supercritical branching random walk at ℤd is investigated.

Keywords

Branching random walklocation of the maximumprediction problem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J55: Local time and additive functionals 60K35: Interacting random processes; statistical mechanics type models; percolation theory

Information

Type
Part 1. Branching processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 25 - 31
Copyright
Copyright © Applied Probability Trust 2004 

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References

[1] Chen, X. (2001). Exact convergence rates for the distribution of particles in branching random walks. Ann. Appl. Prob. 11, 1242–1262.Google Scholar
[2] Harris, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.CrossRefGoogle Scholar
[3] Heyde, C. C. (1971). Some almost sure convergence theorems for branching processes. Z. Wahrscheinlichkeitsth. 20, 189–192.Google Scholar
[4] Heyde, C. C. (1971). Some central limit analogues for super-critical Galton-Watson processes. J. Appl. Prob. 8, 52–59.Google Scholar
[5] Heyde, C. C. and Brown, M. M. (1971). An invariance principle and some convergence rate results for branching processes. Z. Wahrscheinlichkeitsth. 20, 271–278.Google Scholar
[6] Revesz, P. (1994). Random Walks of Infinitely Many Particles. World Scientific, Singapore.CrossRefGoogle Scholar