Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment

Abstract : This paper analyses a time-inhomogeneous model with two level of randomness. In the first step a sequence of branching law is sampled independently according to a distribution on point measures. Conditionally on the realisation of this sequence (called environment) we define a branching random walk and find the asymptotic behaviour of its maximal particle. It is of the form V n − ϕ log n + o P (log n), where V n depends on the environment that behaves as a random walk and ϕ > 0 is a constant. It turns out that the logarithmic correction ϕ is bigger than in the homogenous branching case.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, In press, 〈10.1016/j.spa.2018.09.008〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01322464
Contributeur : Bastien Mallein <>
Soumis le : samedi 29 septembre 2018 - 10:57:20
Dernière modification le : mardi 19 mars 2019 - 01:19:04
Document(s) archivé(s) le : lundi 31 décembre 2018 - 10:36:42

Fichier

brwre.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Bastien Mallein, Piotr Miłoś. Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment. Stochastic Processes and their Applications, Elsevier, In press, 〈10.1016/j.spa.2018.09.008〉. 〈hal-01322464v2〉

Partager

Métriques

Consultations de la notice

22

Téléchargements de fichiers

23