On a Transformation of Analytic Characteristic Functions
On bounds for the characteristic functions of some degenerate multidimensional distributions.
On certain classes of distributions
On characteristic functions of kth record values from the generalized extreme value distribution and its characterization
Recurrence relations for the marginal, joint and conditional characteristic functions of kth record values from the generalized extreme value distribution are established. These relations are utilized to obtain recurrence relations for single, product and conditional moments of kth record values. Moreover, by making use of the recurrence relations the generalized extreme value distribution is characterized.
On independent times and positions for Brownian motions.
On martingales which are finite sums of independent random variables with time dependent coefficients
On normal domination of (super)martingales.
On probability generating functions for matching and occupancy distributions
On revelation transforms that characterize probability distributions.
On small deviation probabilities of positive random variables.
On some generalization of the t-transformation
Using the Nevanlinna representation of the reciprocal of the Cauchy transform of probability measures, we introduce a two-parameter transformation of probability measures on the real line ℝ, which is another possible generalization of the t-transformation. Using that deformation we define a new convolution by deformation of the free convolution. The central limit measure with respect to the -deformed free convolutions is still a Kesten measure, but the Poisson limit depends on the two parameters...
On some limit distributions for geometric random sums
We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward...
On the Bennett–Hoeffding inequality
The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an...
On the compound α(t)-modified Poisson distribution
In this paper we introduce compound α(t)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound α(t)-modified Poisson distribution. The characteristics of α(t)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are presented.
On the infinite divisibility of scale mixtures of symmetric α-stable distributions, α ∈ (0,1]
The paper contains a new and elementary proof of the fact that if α ∈ (0,1] then every scale mixture of a symmetric α-stable probability measure is infinitely divisible. This property is known to be a consequence of Kelker's result for the Cauchy distribution and some nontrivial properties of completely monotone functions. It is known that this property does not hold for α = 2. The problem discussed in the paper is still open for α ∈ (1,2).
On the Laplace Transforms of Logconcave Densities
On the quadratic Wiener functional associated with the Malliavin derivative of the square norm of Brownian sample path on interval.
On the spectrum of a distribution function and on unique factorization.
On the Unimodality and self-Decomposability of Certain Transformed Distributions
On Wiener–Hopf factors for stable processes
We give a series representation of the logarithm of the bivariate Laplace exponent κ of α-stable processes for almost all α ∈ (0, 2].