### A completeness theorem for two-parameter stochastic processes

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We define a notion of delta-variance maximization and show it implies epsilon-proximity in expactations.

This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.

This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner.

The aim of this paper is to survey and discuss, very briefly, some ways how to introduce, within the framework of possibilistic measures, a notion analogous to that of conditional probability measure in probability theory. The adjective “analogous” in the last sentence is to mean that the conditional possibilistic measures should play the role of a mathematical tool to actualize one’s degrees of beliefs expressed by an a priori possibilistic measure, having obtained some further information concerning...

We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.

Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination...

Introducimos en este trabajo el concepto de submedida C (comparativa), sobre un álgebra de conjuntos D, estudiamos propiedades de estas submedidas que serán necesarias para la cuantificación de probabilidades comparativas (P.C.) y se relacionan con otro concepto introducido recientemente por Dobrakov, que es el de submedida I. Se estudian las condiciones bajo las que la convergencia de una sucesión (An) en D subordina la convergencia de (An, ≥) y la representación cuantitativa de P.C. mediante submedidas...

In this paper, we study basic properties of symmetric stable random vectors for which the spectral measure is a copula, i.e., a distribution having uniformly distributed marginals.