Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.
Hypercontractivity of simple random variables
The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.
Hyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approach
In previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.
Idempotent versions of Haar’s Lemma: links between comparison of discrete event systems with different state spaces and control
Haar's Lemma (1918) deals with the algebraic characterization of the inclusion of polyhedral sets. This Lemma has been involved many times in automatic control of linear dynamical systems via positive invariance of polyhedrons. More recently, it has been used to characterize stochastic comparison w.r.t. linear/integral ordering of Markov (reward) chains. In this paper we develop a state space oriented approach to the control of Discrete Event Systems (DES) based on the remark that most of control...
Improved inclusion-exclusion identities and inequalities based on a particular class of abstract tubes.
Improved ratio inequalities for martingales
Inégalité de Brunn-Minkowski-Lusternik, et autres inégalités géométriques et fonctionnelles
La théorie des corps convexes a commencé à la fin du xixe siècle avec l’inégalité de Brunn, généralisée ensuite sous la forme de l’inégalité de Brunn-Minkowski-Lusternik, qui s’applique à des ensembles non convexes. Ce thème a depuis longtemps des contacts avec les problèmes isopérimétriques et avec des inégalités d’Analyse telle que les plongements de Sobolev. On développera quelques aspects plus récents des inégalités géométriques, dont certains sont liés à la technique du transport de mesure,...
Inégalités de convexité pour les processus croissants et les sousmartingales
Inégalités de corrélation sur et dans
Inégalités en norme pour le produit des suprema de plusieurs martingales arrêtées à des temps aléatoires. Inégalités avec poids
Inégalités isopérimétriques en analyse et probabilités
Inégalités isopérimétriques et calcul stochastique
Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes
Inégalités pour les processus self-similaires arrêtés à un temps quelconque
Inequalities between hypergeometric tails.
Inequalities for sums of independent geometrical random variables.
Inequalities for Walsh like random variables.
Inequalities of Bonferroni-Galambos type with applications to the Tutte polynomial and the chromatic polynomial.
Infimum-convolution description of concentration properties of product probability measures, with applications
Information-type divergence when the likelihood ratios are bounded
The so-called ϕ-divergence is an important characteristic describing "dissimilarity" of two probability distributions. Many traditional measures of separation used in mathematical statistics and information theory, some of which are mentioned in the note, correspond to particular choices of this divergence. An upper bound on a ϕ-divergence between two probability distributions is derived when the likelihood ratio is bounded. The usefulness of this sharp bound is illustrated by several examples of...