A Boolean-valued probability theory
A characterization of α-convolutions
A completeness theorem for two-parameter stochastic processes
A counterexample on generalized convolutions
A Family of Measures of Uncertainty Involving Utilities: Definition, Properties, Applications and Statistical Inferences.
A Gauss-Kuzmin-Lévy theorem for a certain continued fraction.
A general bounded continuous moment problem and its sets of uniqueness
A geometric approach to measuring dependence between random vectors
A Lemma on Proximity of Variances and Expectations
We define a notion of delta-variance maximization and show it implies epsilon-proximity in expactations.
A lemma on proximity of variances and expectations
A Logic for Reasoning About Qualitative Probability
A noncompact Choquet theorem
A nonstandard modification of Dempster combination rule
It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like...
A note on nonaxiomatizability of independence relations generated by certain probabilistic structures
A Note on Quasicontinuous Kernels Representing Quasi-Linear Positive Maps.
A note on strong laws of large numbers for dependent random sets and fuzzy random sets.
A note on the interval-valued marginal problem and its maximum entropy solution
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.
A probabilistic ergodic decomposition result
Let be a standard probability space. We say that a sub-σ-algebra of decomposes μ in an ergodic way if any regular conditional probability with respect to andμ satisfies, for μ-almost every x∈X, . In this case the equality , gives us an integral decomposition in “-ergodic” components. For any sub-σ-algebra of , we denote by the smallest sub-σ-algebra of containing and the collection of all setsAin satisfyingμ(A)=0. We say that isμ-complete if . Let be a non-empty family...
A property of doubly stochastic densities
A remark on metrics for finitely additive distribution functions.