Transportation cost-information and concentration inequalities for bifurcating Markov chains

We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cos...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2017-10, Vol.23 (4B), p.3213-3242
Hauptverfasser: Bitseki Penda, Siméon Valère, Escobar-Bach, Mikael, Guillin, Arnaud
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives birth to two offsprings in the next one. Transportation cost inequalities provide useful concentra-tion inequalities. We also study deviation inequalities for the empiri-cal means under relaxed assumptions on the Wasserstein contraction of the Markov kernels. Applications to bifurcating non linear autore-gressive processes are considered: deviation inequalities for pointwise estimates of the non linear leading functions.
ISSN:1350-7265
DOI:10.3150/16-BEJ843