Ergodic theorem for branching Markov chains indexed by trees with arbitrary shape - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Ergodic theorem for branching Markov chains indexed by trees with arbitrary shape

Résumé

We prove an ergodic theorem for Markov chains indexed by the Ulam-Harris-Neveu tree over large subsets with arbitrary shape under two assumptions: with high probability, two vertices in the large subset are far from each other and have their common ancestor close to the root. The assumption on the common ancestor can be replaced by some regularity assumption on the Markov transition kernel. We verify that those assumptions are satisfied for some usual trees. Finally, with Markov-Chain Monte-Carlo considerations in mind, we prove when the underlying Markov chain is stationary and reversible that the Markov chain, that is the line graph, yields minimal variance for the empirical average estimator among trees with a given number of nodes.
Fichier principal
Vignette du fichier
article_thm_ergodique.pdf (263.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04517492 , version 1 (22-03-2024)

Identifiants

Citer

Julien Weibel. Ergodic theorem for branching Markov chains indexed by trees with arbitrary shape. 2024. ⟨hal-04517492⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More