Sur les fonctions extrémales des inégalités de Sobolev des opérateurs de diffusion
Sur les lois à symétrie elliptique
Sur les précisions comparées de la moyenne et de la médiane
Sur les solutions d'une équation fonctionnelle non linéaire de B. Mandelbrot
Sur l'inégalité de Sobolev logarithmique des opérateurs de Laguerre à petit paramètre
Sur quelques aspects combinatoires du calcul des probabilités
Sur quelques inégalités entre les moments absolus d'ordre positif d'une suite de variables aléatoires indépendantes et le second théorème — limite du calcul des probabilités au domaine de la loi de Laplace — Gauss dans la formulation de Liapounoff. I
Sur quelques inégalités entre les moments absolus d'ordre positif d'une suite de variables aléatoires indépendantes et le second théorème — limite du calcul des probabilités au domaine de la loi de Laplace — Gauss dans la formulation de Liapounoff. II
Sur une extension de la notion de loi semi-stable
Sur une généralisation du problème de l'ajustement d'une mesure à des marges
Symmetric partitions and pairings
The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.
Symmetrization of Bernoulli.
Symmetrization of probability measures, pushforward of order 2 and the Boolean convolution
We study relations between the Boolean convolution and the symmetrization and the pushforward of order 2. In particular we prove that if μ₁,μ₂ are probability measures on [0,∞) then and if ν₁,ν₂ are symmetric then . Finally we investigate necessary and sufficient conditions under which the latter equality holds.
Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails
We present two-sided estimates of moments and tails of polynomial chaoses of order at most three generated by independent symmetric random variables with log-concave tails as well as for chaoses of arbitrary order generated by independent symmetric exponential variables. The estimates involve only deterministic quantities and are optimal up to constants depending only on the order of the chaos variable.
Tail and moment estimates for some types of chaos
Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where are real numbers. We derive approximate formulas for the tails and moments of X and of its decoupled version, which are exact up to some universal constants.
Tail and moment estimates for sums of independent random variables with logarithmically concave tails
For random variables , where is a sequence of symmetric, independent, identically distributed random variables such that is a concave function we give estimates from above and from below for the tail and moments of S. The estimates are exact up to a constant depending only on the distribution of ξ. They extend results of S. J. Montgomery-Smith [MS], M. Ledoux and M. Talagrand [LT, Chapter 4.1] and P. Hitczenko [H] for the Rademacher sequence.
Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case
We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a bivariate subordinator....
Tail orderings and the total time on test transform
The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.
Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws.
Tendency Towards Normality of Linear Combinations of Random Variables.