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Several results on set-valued possibilistic distributions

Ivan Kramosil, Milan Daniel (2015)

Kybernetika

When proposing and processing uncertainty decision-making algorithms of various kinds and purposes, we more and more often meet probability distributions ascribing non-numerical uncertainty degrees to random events. The reason is that we have to process systems of uncertainties for which the classical conditions like σ -additivity or linear ordering of values are too restrictive to define sufficiently closely the nature of uncertainty we would like to specify and process. In cases of non-numerical...

Shift invariant measures and simple spectrum

A. Kłopotowski, M. Nadkarni (2000)

Colloquium Mathematicae

We consider some descriptive properties of supports of shift invariant measures on ℂ ℤ under the assumption that the closed linear span (in L 2 ) of the co-ordinate functions on ℂ ℤ is all of L 2 .

Simple fractions and linear decomposition of some convolutions of measures

Jolanta K. Misiewicz, Roger Cooke (2001)

Discussiones Mathematicae Probability and Statistics

Every characteristic function φ can be written in the following way: φ(ξ) = 1/(h(ξ) + 1), where h(ξ) = ⎧ 1/φ(ξ) - 1 if φ(ξ) ≠ 0 ⎨ ⎩ ∞ if φ(ξ) = 0 This simple remark implies that every characteristic function can be treated as a simple fraction of the function h(ξ). In the paper, we consider a class C(φ) of all characteristic functions of the form φ a ( ξ ) = [ a / ( h ( ξ ) + a ) ] , where φ(ξ) is a fixed characteristic function. Using the well known theorem on simple fraction decomposition of rational functions we obtain that convolutions...

Singleton independence

Luigi Accardi, Yukihiro Hashimoto, Nobuaki Obata (1998)

Banach Center Publications

Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional...

Standard and nonstandard representability of positive uncertainty orderings

Andrea Capotorti, Giulianella Coletti, Barbara Vantaggi (2014)

Kybernetika

Axioms are given for positive comparative probabilities and plausibilities defined either on Boolean algebras or on arbitrary sets of events. These axioms allow to characterize binary relations representable by either standard or nonstandard measures (i. e. taking values either on the real field or on a hyperreal field). We also study relations between conditional events induced by preferences on conditional acts.

Stochastic fuzzy differential equations with an application

Marek T. Malinowski, Mariusz Michta (2011)

Kybernetika

In this paper we present the existence and uniqueness of solutions to the stochastic fuzzy differential equations driven by Brownian motion. The continuous dependence on initial condition and stability properties are also established. As an example of application we use some stochastic fuzzy differential equation in a model of population dynamics.

Stochastic signal codification and sigma transform.

Luis Basañez Villaluenga, Nadal Batle Nicolau, Gabriel Ferraté Pascual, Josep Grané Manlleu, Enric Trillas (1983)

Stochastica

In the last years, a relation between bounded real functions of one variable and two-valued probabilistic functions defined on the complex plane has been established through the introduction of the Sigma-Transform concept.The paper presents an extension of the concept of Sigma-Transform, giving rise to the diagonal Sigma-Transform and the Striped Sigma-Transform which, when combined, allow a formal treatment of the Multichannel Stochastic Signal Codification. An application of the method to error...

Submedidas C y cuantificación de probabilidades comparativas.

César Rodríguez Ortiz (1982)

Trabajos de Estadística e Investigación Operativa

De los axiomas de Villegas para probabilidades comparativas, el de continuidad monótona resulta suficiente para la compatibilidad con una submedida C (Ortiz, 1980, Teo. 8), mientras que el axioma de no existencia de átomos, junto con el anterior, caracteriza la subclase de probabilidades comparativas sin átomos que pueden representarse mediante medidas de probabilidad. El estudio de las propiedades de las submedidas C nos conduce a proponer en este trabajo un nuevo axioma, que junto al de continuidad...

Sum of observables in fuzzy quantum spaces

Anatolij Dvurečenskij, Anna Tirpáková (1992)

Applications of Mathematics

We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.

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