On a class of covariance operators.
On additive and non-additive measures of directed divergence
On an Extendability Problem for Measures.
On analytical properties of generalized convolutions
The paper is, for the most part, devoted to a survey of the analytical properties of generalized convolution algebras and their realizations. This issue appears to be the state of the art until now because intensive research on the generalized convolution and the related models still persists.
On Atoms of Measures on Product Spaces.
On Certain Generalized Probability Domains
On exchangeable random variables and the statistics of large graphs and hypergraphs.
On independent sets in purely atomic probability spaces with geometric distribution.
On limiting towards the boundaries of exponential families
This work studies the standard exponential families of probability measures on Euclidean spaces that have finite supports. In such a family parameterized by means, the mean is supposed to move along a segment inside the convex support towards an endpoint on the boundary of the support. Limit behavior of several quantities related to the exponential family is described explicitly. In particular, the variance functions and information divergences are studied around the boundary.
On products of admissible liftings and densities.
On some properties of the Lüroth-type alternating series representations for real numbers.
On the approximation properties of Bernstein polynomials via probabilistic tools.
On the Borel-Cantelli Lemma and moments
We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., A generalization of the Borel-Cantelli Lemma, Statist. Probab. Lett. 67 (2004), no. 3, 233–239.
On the dimension of an irrigable measure
On the existence of conditional density functions
On the existence of disintegrations
On the Gaussian random matrix ensembles with additional symmetry conditions.
On the range of purely atomic probability measures
Operator valued probability theory.
Optimal solutions of multivariate coupling problems
Some necessary and some sufficient conditions are established for the explicit construction and characterization of optimal solutions of multivariate transportation (coupling) problems. The proofs are based on ideas from duality theory and nonconvex optimization theory. Applications are given to multivariate optimal coupling problems w.r.t. minimal -type metrics, where fairly explicit and complete characterizations of optimal transportation plans (couplings) are obtained. The results are of interest...