Survival probabilities for branching Brownian motion with absorption.
The distribution of trees.
The martingale Smirnov class.
The smallest g-supermartingale and reflected BSDE with single and double obstacles
Théorèmes limites avec poids pour les martingales vectorielles à temps continu
On développe une approche générale du théorème limite centrale presque-sûre pour les martingales vectorielles quasi-continues à gauche convenablement normalisées dont on dégage une extension quadratique et un nouveau théorème de la limite centrale. L'application de ce résultat à l'estimation de la variance d'un processus à accroissements indépendants et stationnaires illustre l'usage qu'on peut en faire en statistique.
Théorie de Littlewood-Paley-Stein et processus stables
Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function
Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that 𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,..., 𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,.... The first inequality is sharp, and it is strict in all nontrivial cases.
Two-parameter multipliers on hardy spaces
Une définition faible de BMO
Une version probabiliste d'un théorème d'interpolation de G. Stampacchia
Universally measurable spaces: an invariance theorem and diverse characterizations
Vector-Valued Singular Integrals Revisited-with Random Dyadic Cubes
The vector-valued T(1) theorem due to Figiel, and a certain square function estimate of Bourgain for translations of functions with a limited frequency spectrum, are two cornerstones of harmonic analysis in UMD spaces. In this paper, a simplified approach to these results is presented, exploiting Nazarov, Treil and Volberg's method of random dyadic cubes, which allows one to circumvent the most subtle parts of the original arguments.
Wavelet constructions in non-linear dynamics.
Weak type estimates associated to Burkholder's martingale inequality.
Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
Об обобщении неравенств Нагаева-Фука на некоторый класс случайных полей.