Contributions to foundations of probability calculus on the basis of the modal logical calculus or
Contributions to foundations of probability calculus on the basis of the modal logical calculus or
Correction to: “A note on nonaxiomatizability of independence relations generated by certain probabilistic structures”
Démonstration élémentaire d'une proposition générale de la théorie des probabilités.
Desintegration and compact measures.
Désintégrations réguliéres, tribus fortes, et probalités extrémales
Duality for generalized events
Dynamic dependence ordering for Archimedean copulas and distorted copulas
This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i. e. given remaining lifetimes , to compare the dependence of given , and given , where . More precisely, analytical results will be obtained in the case the survival copula of is either Archimedean or a distorted copula. The case of a frailty based model will also be discussed in details.
Ein massentheoretisches Marginalproblem.
Einführung des Wahrscheinlichkeitsoperators durch Postulate.
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.
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...
Existence of Conditional Probabilities.
Existence of nontrivial stochastic monoids.
Filosofická pojetí pravděpodobnosti v pracích českých myslitelů [Book]
Fuzzification of crisp domains
The present paper is devoted to the transition from crisp domains of probability to fuzzy domains of probability. First, we start with a simple transportation problem and present its solution. The solution has a probabilistic interpretation and it illustrates the transition from classical random variables to fuzzy random variables in the sense of Gudder and Bugajski. Second, we analyse the process of fuzzification of classical crisp domains of probability within the category of -posets of fuzzy...
Generalization of some results on the degree of progress to goal in self-organization process
Generated fuzzy implications and fuzzy preference structures
The notion of a construction of a fuzzy preference structures is introduced. The properties of a certain class of generated fuzzy implications are studied. The main topic in this paper is investigation of the construction of the monotone generator triplet , which is the producer of fuzzy preference structures. Some properties of mentioned monotone generator triplet are investigated.
Infinite pseudo-random sequences of high algorithmic complexity
Le concept nouveau de fonctionnelle d'opacité d'une statistique. Étude des relations entre la loi des grands nombres, l'entropie informationnelle et l'entropie statistique