Random matrices, magic squares and matching polynomials.
Relèvement borélien compatible avec une classe d'ensembles négligeables. Application à la désintégration des mesures
Remarques sur les classes de Vapnik-Cervonenkis
Representation of Itô integrals by Lebesgue/Bochner integrals
In [Yong 2004], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later...
Sample behavior and laws of large numbers for Gaussian random elements.
Semigroup actions on tori and stationary measures on projective spaces
Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits...
Semi-groupes holomorphes et -convexité
Semi-groupes holomorphes et -convexité (suite)
Sequences or random variables in Lp for p<1.
Some results on the continuity of stable processes and the domain of attraction of continuous stable processes
Some results on the span of families of Banach valued independent, random variables.
Strong laws of large numbers for arrays of row-wise exchangeable random elements.
Strong laws of large numbers for -valued random fields.
Strong laws of large numbers for weighted sums of random elements in normed linear spaces.
Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of [Book]
Sur certaines propriétés des espaces de Banach et
Sur la comparaison d'une mesure μ dans un espace vectoriel X avec ses translatées
Sur la régularité de certaines fonctions aléatoires d'Ornstein-Uhlenbeck
Sur les espaces de Fréchet ne contenant pas
Soit E un espace de Fréchet séparable ne contenant pas ; soit de plus une suite symétrique de vecteurs aléatoires à valeurs dans E. Alors si la série de Fourier aléatoire , , a p.s. ses sommes partielles localement uniformément bornées dans E, nécessairement elle converge p.s. uniformément sur tout compact de vers une fonction aléatoire à valeurs dans E et à trajectoires continues.
Tail and moment estimates for sums of independent random vectors with logarithmically concave tails
Let be a sequence of independent symmetric real random variables with logarithmically concave tails. We consider a variable , where are vectors of some Banach space. We derive approximate formulas for the tail and moments of ∥X∥. The estimates are exact up to some universal constant and they extend results of S. J. Dilworth and S. J. Montgomery-Smith [1] for the Rademacher sequence and E. D. Gluskin and S. Kwapień [2] for real coefficients.