Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2014

Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes

Résumé

We give asymptotic spectral results for Gram matrices of the form n −1 X n X T n where the entries of X n are dependent across both rows and columns and that are functionals of absolutely regular sequences and have only finite second moments. We derive, under mild dependence conditions in addition to an arithmetical decay condition on the β-mixing coefficients, an integral equation of the Stieltjes transform of the limiting spectral distribution of n −1 X n X T n in terms of the spectral density of the underlying process. Applications to examples of positive recurrent Markov chains and dynamical systems are also given.
Fichier principal
Vignette du fichier
1406.6011v2.pdf (230.78 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01076757 , version 1 (23-10-2014)

Identifiants

Citer

Marwa Banna. Limiting spectral distribution of Gram matrices associated with functionals of β-mixing processes. 2014. ⟨hal-01076757⟩
34 Consultations
138 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More