Measurability of stochastic process and approximate continuity of its correlation function.
Measure attractors for stochastic Navier-Stokes equations.
Measures defined by Markov times
Median for metric spaces
We consider a Köthe space of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications....
Meilleures approximations et médianes conditionnelles
Mesurabilité des débuts et théorème de section : le lot à la portée de toutes les bourses
Mesure de Hausdorff de la trajectoire de certains processus à accroissements indépendants et stationnaires
Mesures à accroissements indépendants et P.A.I. non homogènes
Mesures aléatoires localement finies
Mesures aléatoires stationnaires et mesure de Palm
Mesures aléatoires stationnaires sur un espace produit
Mesures aléatoires -régulières
Mesures de Radon sur et mesures cylindriques
Mesures singulières associées à des découpages aléatoires d'un hypercube
Mesures vectorielles dans les espaces réticulés
Metric diophantine approximation and probability.
Metric entropy of convex hulls in Hilbert spaces
Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), , , by functions of the ’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences .
Metric projections and best approximants in Bochner-Orlicz spaces.
In the first section of this paper there are given criteria for strict convexity and smoothness of the Bochner-Orlicz space with the Orlicz norm as well as the Luxemburg norm. In the second one that geometrical properties are applied to the characterization of metric projections and zero mean valued best approximants to Bochner-Orlicz spaces.
Metric unconditionality and Fourier analysis
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
Métrisabilité de quelques espaces de processus aléatoires