Ein massentheoretisches Marginalproblem.
Einführung des Wahrscheinlichkeitsoperators durch Postulate.
El valor difuso esperado con integrales semiconormadas.
In this paper we first use the semiconormed fuzzy integrals in order to extend the definition of the fuzzy expected value (F.E.V.) (Kandel, 1979). We generalize some of the properties due to Kandel with a criticism about his purpose of constraining the F.E.V. to be linear. Finally, a necessary and sufficient condition is given in order to guarantee some linearity properties for any semiconormed fuzzy integral.
Éléments de probabilités quantiques (exposés I à V)
Éléments de probabilités quantiques (exposés IX et X)
Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes
Equipartitioning Common Domains of Non-Atomic Measures.
Equivalence of Gaussian measures of finite sum of stochastic processes
Equivalent or absolutely continuous probability measures with given marginals
Let (X,A) and (Y,B) be measurable spaces. Supposewe are given a probability α on A, a probability β on B and a probability μ on the product σ-field A ⊗ B. Is there a probability ν on A⊗B, with marginals α and β, such that ν ≪ μ or ν ~ μ ? Such a ν, provided it exists, may be useful with regard to equivalent martingale measures and mass transportation. Various conditions for the existence of ν are provided, distinguishing ν ≪ μ from ν ~ μ.
Espaces de Lebesgue
Espérances conditionnelles d'intégrandes semi-continus
Esperanza condicionada para probabilidades finitamente aditivas.
Let (Ω, θ, J) be a finitely additive probabilistic space formed by any set Ω, an algebra of subsets θ and a finitely additive probability J. In these conditions, if F belongs to V1(Ω, θ, J) there exists f, element of the completion of L1(Ω, θ, J), such that F(E) = ∫E f dJ for all E of θ and conversely.The integral representation gives sense to the following result, which is the objective of this paper, in terms of the point function: if β is a subalgebra of θ, for every F of V1(Ω, θ, J) there exists...
Estimates of Hellinger integrals of infinitely divisible distributions
Events of Borel Sets, Construction of Borel Sets and Random Variables for Stochastic Finance
We consider special events of Borel sets with the aim to prove, that the set of the irrational numbers is an event of the Borel sets. The set of the natural numbers, the set of the integer numbers and the set of the rational numbers are countable, so we can use the literature [10] (pp. 78-81) as a basis for the similar construction of the proof. Next we prove, that different sets can construct the Borel sets [16] (pp. 9-10). Literature [16] (pp. 9-10) and [11] (pp. 11-12) gives an overview, that...
Exchanging the order of taking suprema and countable intersections of σ-algebras
Existence of Conditional Probabilities.
Existence of nontrivial stochastic monoids.
Existence theorems for measures on continous posets, with applications to random set theory.
Expectation, conditional expectation and martingales in local fields.
Expected values in the alternative set theory and their applications to some limit theorems
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.