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Sample d -copula of order m

José M. González-Barrios, María M. Hernández-Cedillo (2013)

Kybernetika

In this paper we analyze the construction of d -copulas including the ideas of Cuculescu and Theodorescu [5], Fredricks et al. [15], Mikusiński and Taylor [25] and Trutschnig and Fernández-Sánchez [33]. Some of these methods use iterative procedures to construct copulas with fractal supports. The main part of this paper is given in Section 3, where we introduce the sample d -copula of order m with m ≥ 2 , the central idea is to use the above methodologies to construct a new copula based on a sample. The...

Semi-recorrido condicionado (expresión asintótica de la r-esperanza condicionada).

Juan Antonio Cuesta Albertos, Carlos Matrán Bea (1983)

Trabajos de Estadística e Investigación Operativa

In a probability space (Ω,σ,P), for α ⊂ σ a sub-σ field, in general the best approximation in L∞ by elements of L∞(α) has not a unique solution. For the election between these, we prove the convergence P-almost surely of the conditional r-means, when r → ∞, to one solution, which we call conditional mid-range. This is characterized for each ω ∈ Ω by the mid-range, of one regular conditional distribution Q(ω, ·).

Sets with doubleton sections, good sets and ergodic theory

A. Kłopotowski, M. G. Nadkarni, H. Sarbadhikari, S. M. Srivastava (2002)

Fundamenta Mathematicae

A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.

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.

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