Calcul des probabilités - Théorème des grands écarts et théorème de la limite centrale pour certains produits de matrices aléatoires
Théorèmes limites pour les produits de matrices aléatoires
Théorèmes de renouvellement pour les produits de matrices aléatoires Équations aux différences aléatoires
Répartition d'état d'un opérateur de Schrödinger aléatoire Distribution empirique des valeurs propres d'une matrice de Jacobi
Théorèmes des grands écarts sur les groupes nilpotents simplement connexes
Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications
A Local Limit Theorem on the Semi-Direct Product of and
A local limit theorem on the semi-direct product of and
Local limit theorems on some non unimodular groups.
Let Gd be the semi-direct product of R*+ and Rd, d ≥ 1 and let us consider the product group Gd,N = Gd x RN, N ≥ 1. For a large class of probability measures μ on Gd,N, one prove that there exists ρ(μ) ∈ ]0,1] such that the sequence of finite measures {(n(N+3)/2 / ρ(μ)n) μ*n}...
On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...
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