On the scooping property of measures by means of disjoint balls
On two definitions of the integral of a p-adic function
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On -porous sets in abstract spaces.
Operator-valued Feynman integral via conditional Feynman integrals on a function space
Let C 0r [0; t] denote the analogue of the r-dimensional Wiener space, define X t: C r[0; t] → ℝ2r by X t (x) = (x(0); x(t)). In this paper, we introduce a simple formula for the conditional expectations with the conditioning function X t. Using this formula, we evaluate the conditional analytic Feynman integral for the functional , where η is a complex Borel measure on [0, t], and θ(s, ·) and φ are the Fourier-Stieltjes transforms of the complex Borel measures on ℝr. We then introduce an integral...
Partial differential systems of generalized Wiener and Feynman integrals
Physical states on quantum logics. I
Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups
Poisson Random Fields with Control Measures. I
Prevalence of some known typical properties.
Probabilités cylindriques et processus linéaires
Probability measures with big kernels.
Problèmes ergodiques dans la théorie quantique des champs
Processus canoniquement mesurables (ou : Doob avait raison)
Processus de Markov et désintégrations régulières
Un théorème classique exprime qu’à partir d’un semi-groupe d’opérateurs sur l’espace des fonctions continues tendant vers 0 à l’infini, , , , continue, , on peut construire un processus markovien “standard”, à trajectoires réglées et continues à droite, quasi-continu à gauche ; l’espace des états est supposé localement compact à base dénombrable d’ouverts. Nous supposons ici que l’espace des états est seulement universellement mesurable dans un souslinien complètement régulier ; le processus...
Prodistributions
Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
This work is devoted to the concept of statistical solution of the Navier-Stokes equations, proposed as a rigorous mathematical object to address the fundamental concept of ensemble average used in the study of the conventional theory of fully developed turbulence. Two types of statistical solutions have been proposed in the 1970’s, one by Foias and Prodi and the other one by Vishik and Fursikov. In this article, a new, intermediate type of statistical solution is introduced and studied. This solution...
Propriété de trace en dimension infinie d'espaces du type Sobolev
Proprites de Radon-Nikodym pour les cones positifs de mesures.
Quelques espaces fonctionnels associés à des processus gaussiens
The first part of the paper presents results on Gaussian measures supported by general Banach sequence spaces and by particular spaces of Besov-Orlicz type. In the second part, a new constructive isomorphism between the just mentioned sequence spaces and corresponding function spaces is established. Consequently, some results on the support function spaces for the Gaussian measure corresponding to the fractional Brownian motion are proved. Next, an application to stochastic equations is given. The...