Precise large deviation asymptotics for products of random matrices - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2020

Precise large deviation asymptotics for products of random matrices

Résumé

Let $(g_{n})_{n\geq 1}$ be a sequence of independent identically distributed $d\times d$ real random matrices with Lyapunov exponent $\lambda$. For any starting point $x$ on the unit sphere in $\mathbb R^d$, we deal with the norm $ | G_n x | $, where $G_{n}:=g_{n} \ldots g_{1}$. The goal of this paper is to establish precise asymptotics for large deviation probabilities $\mathbb P(\log | G_n x | \geq n(q+l))$, where $q>\lambda$ is fixed and $l$ is vanishing as $n\to \infty$. We study both invertible matrices and positive matrices and give analogous results for the couple $(X_n^x,\log | G_n x |)$ with target functions, where $X_n^x= G_n x /| G_n x |$. As applications we improve previous results on the large deviation principle for the matrix norm $\|G_n\|$ and obtain a precise local limit theorem with large deviations.
Fichier principal
Vignette du fichier
LDNormCocy004.pdf (485.36 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02173735 , version 1 (04-07-2019)

Identifiants

  • HAL Id : hal-02173735 , version 1

Citer

Hui Xiao, Ion Grama, Quansheng Liu. Precise large deviation asymptotics for products of random matrices. Stochastic Processes and their Applications, 2020, 130, pp.5213-5242. ⟨hal-02173735⟩
63 Consultations
59 Téléchargements

Partager

Gmail Facebook X LinkedIn More