Branching random walk with a random environment in time

We consider a branching random walk on \(\mathbb{R}\) with a stationary and ergodic environment \(\xi=(\xi_n)\) indexed by time \(n\in\mathbb{N}\). Let \(Z_n\) be the counting measure of particles of generation \(n\). For the case where the corresponding branching process \(\{Z_n(\mathbb{R})\}\) \(...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Huang, Chunmao, Liu, Quansheng
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 29.07.2014
Subjects
Position measurement
Random walk
Random walk theory
Theorems
Online AccessGet full text

Cover

More Information
Summary:We consider a branching random walk on \(\mathbb{R}\) with a stationary and ergodic environment \(\xi=(\xi_n)\) indexed by time \(n\in\mathbb{N}\). Let \(Z_n\) be the counting measure of particles of generation \(n\). For the case where the corresponding branching process \(\{Z_n(\mathbb{R})\}\) \( (n\in\mathbb{N})\) is supercritical, we establish large deviation principles, central limit theorems and a local limit theorem for the sequence of counting measures \(\{Z_n\}\), and prove that the position \(R_n\) (resp. \(L_n\)) of rightmost (resp. leftmost) particles of generation \(n\) satisfies a law of large numbers.
ISSN:2331-8422