Le dual de : démonstrations probabilistes
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....
Central limit theorems with hypotheses in terms of -entropy are proved first in where is a compact metric space and then in an arbitrary separable Banach space.
est un processus de Markov sur un espace localement compact, et est une fonction excessive. Soit une famille de temps d’arrêt est -harmonique si pour tout , pour tout temps d’arrêt appartenant à . est un potentiel si sa plus grande minorante forte -harmonique est nulle. La plus grande minorante forte -harmonique de est égale à la somme de deux fonctions excessives qui sont étudiées. On déduit différentes caractérisations des -potentiels suivant les propriétés de la famille...
Multistage stochastic optimization requires the definition and the generation of a discrete stochastic tree that represents the evolution of the uncertain parameters in time and space. The dimension of the tree is the result of a trade-off between the adaptability to the original probability distribution and the computational tractability. Moreover, the discrete approximation of a continuous random variable is not unique. The concept of the best discrete approximation has been widely explored and...