Corrigenda to “Operator semi-stable probability measures on ”
Corrigendum to the paper "Semigroup actions on tori and stationary measures on projective spaces" (Studia Math. 171 (2005), 33-66)
Cylindrical measures on tensor products of Banach spaces and random linear operators.
Cylindrical Measures on Vector Lattices and Random Measures.
Decomposability of Cylindrical Martingales and Absolutely Summing Operators.
Deux exemples d'utilisation de mesures majorantes
Embedding of random vectors into continuous martingales
Let E be a real, separable Banach space and denote by the space of all E-valued random vectors defined on the probability space Ω. The following result is proved. There exists an extension of Ω, and a filtration on , such that for every there is an E-valued, continuous -martingale in which X is embedded in the sense that a.s. for an a.s. finite stopping time τ. For E = ℝ this gives a Skorokhod embedding for all , and for general E this leads to a representation of random vectors as...
Estimation and tests of the discrete probability law based on the empirical generating function, (two dimensional case).
Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
Fonctions aléatoires gaussiennes, les résultats récents de M. Talagrand
Gaussian measures and the density theorem
Gaussian measures on spaces,
Geometric decomposability properties of probability measures
Hypercontractivity and comparison of moments of iterated maxima and minima of independent random variables.
Infinitely divisible cylindrical measures on Banach spaces
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on...
Integrals related to stationary processes and cylindrical martingales
Isoperimetric problem for uniform enlargement
We consider an isoperimetric problem for product measures with respect to the uniform enlargement of sets. As an example, we find (asymptotically) extremal sets for the infinite product of the exponential measure.
La convergence en loi pour les processus à valeurs dans un espace nucléaire
Large deviations in spaces of stable type
Lévy's probability measures on Banach spaces