Central limit problem and invariance principles on Banach spaces
Central limit problem for symmetric case: Convergence to non-Gaussian laws
Chaos multiplicatif : un traitement simple et complet de la fonction de partition
Complete convergence for -valued -mixingale sequences.
Complete convergence for sums of arrays of random elements.
Complete convergence for weighted sums of arrays of random elements.
Complete convergence in mean for double arrays of random variables with values in Banach spaces
The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order ). In this paper, we give some new results of complete convergence in mean of order and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.
Complete convergence of weighted sums in Banach spaces and the bootstrap mean.
Conditional symmetries of stable measures on
Convergence in Dirichlet law of certain stochastic integrals.
Convergence in mean of weighted sums of -compactly uniformly integrable random elements in Banach spaces.
Convergence of weighted sums of random variables in vector lattices
Convergence presque sûre de martingales multivoques
Corrections : “Domains of attraction in Banach spaces”
Domains of attraction in Banach spaces
Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand
Gaussian Random Series on Metric Vector Spaces.
Hölderian invariance principle for Hilbertian linear processes
Let be the polygonal partial sums processes built on the linear processes , n ≥ 1, where are i.i.d., centered random elements in some separable Hilbert space and the ai's are bounded linear operators , with . We investigate functional central limit theorem for in the Hölder spaces of functions such that ||x(t + h) - x(t)|| = o(p(h)) uniformly in t, where p(h) = hαL(1/h), 0 ≤ h ≤ 1 with 0 ≤ α ≤ 1/2 and L slowly varying at infinity. We obtain the weak convergence of ...
Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix
This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...
Inégalités isopérimétriques en analyse et probabilités