Deviation inequalities for separately Lipschitz functionals of iterated random functions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2015

Deviation inequalities for separately Lipschitz functionals of iterated random functions

Jérôme Dedecker
  • Fonction : Auteur
  • PersonId : 900512
Xiequan Fan
  • Fonction : Auteur
  • PersonId : 948530

Résumé

We consider a Markov chain X_1, X_2, ..., X_n belonging to a class of iterated random functions, which is ''one-step contracting" with respect to some distance d. If f is any separately Lipschitz function with respect to d, we use a well known decomposition of S_n=f(X_1, ..., X_n) -E[f(X_1, ... , X_n)]$ into a sum of martingale differences d_k with respect to the natural filtration F_k. We show that each difference d_k is bounded by a random variable eta_k independent of F_{k-1}. Using this very strong property, we obtain a large variety of deviation inequalities for S_n, which are governed by the distribution of the eta_k's. Finally, we give an application of these inequalities to the Wasserstein distance between the empirical measure and the invariant distribution of the chain.
Fichier principal
Vignette du fichier
McDiterated 11.pdf (263.17 Ko) Télécharger le fichier
McDiteratedRevised.pdf (272.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00948216 , version 1 (17-02-2014)
hal-00948216 , version 2 (17-10-2014)

Identifiants

Citer

Jérôme Dedecker, Xiequan Fan. Deviation inequalities for separately Lipschitz functionals of iterated random functions. Stochastic Processes and their Applications, 2015, 125 (1), pp.60-90. ⟨hal-00948216v2⟩
580 Consultations
827 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More