The spread of a catalytic branching random walk

Philippe Carmona; Yueyun Hu

Annales de l'I.H.P. Probabilités et statistiques (2014)

  • Volume: 50, Issue: 2, page 327-351
  • ISSN: 0246-0203

Abstract

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We consider a catalytic branching random walk on ℤ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position M n : For some constant α , M n n → α almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for M n - α n as n goes to infinity.

How to cite

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Carmona, Philippe, and Hu, Yueyun. "The spread of a catalytic branching random walk." Annales de l'I.H.P. Probabilités et statistiques 50.2 (2014): 327-351. <http://eudml.org/doc/271969>.

@article{Carmona2014,
abstract = {We consider a catalytic branching random walk on $\mathbb \{Z\} $ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_\{n\}$: For some constant $\alpha $, $\frac\{M_\{n\}\}\{n\}\rightarrow \alpha $ almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for $M_\{n\}-\alpha n$ as $n$ goes to infinity.},
author = {Carmona, Philippe, Hu, Yueyun},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {branching processes; catalytic branching random walk; branching process},
language = {eng},
number = {2},
pages = {327-351},
publisher = {Gauthier-Villars},
title = {The spread of a catalytic branching random walk},
url = {http://eudml.org/doc/271969},
volume = {50},
year = {2014},
}

TY - JOUR
AU - Carmona, Philippe
AU - Hu, Yueyun
TI - The spread of a catalytic branching random walk
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2014
PB - Gauthier-Villars
VL - 50
IS - 2
SP - 327
EP - 351
AB - We consider a catalytic branching random walk on $\mathbb {Z} $ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_{n}$: For some constant $\alpha $, $\frac{M_{n}}{n}\rightarrow \alpha $ almost surely on the set of infinite number of visits of the origin. Then we determine all possible limiting laws for $M_{n}-\alpha n$ as $n$ goes to infinity.
LA - eng
KW - branching processes; catalytic branching random walk; branching process
UR - http://eudml.org/doc/271969
ER -

References

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