For arbitrary Borel probability measures on the real line, necessary and sufficient conditions
are presented that characterize best purely atomic approximations relative to the classical …

For arbitrary Borel probability measures on the real line, necessary and sufficient conditions
are presented that characterize best purely atomic approximations relative to the classical …

This paper studies best finitely supported approximations of one-dimensional probability
measures with respect to the L r-Kantorovich (or transport) distance, where either the …

This thesis is based on four papers. The first two papers fall into the field of approximation of
one-dimensional probabilities, the third into uniform distribution theory, and the last paper …

Let (ξ, η) be a bivariate Lévy process such that the integral\int_0^ ∞ e^-ξ _ td η _t converges
almost surely. We characterise, in terms of their Lévy measures, those Lévy processes for …

In the one-dimensional case Rio (Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009) 802–
817) gave a concise bound for the central limit theorem in the Vaserstein distances, which is …

Let (ξ, η) be a bivariate Lévy process such that the integral∫ 0∞ e-ξ t-dη t converges almost
surely. We characterise, in terms of their Lévy measures, those Lévy processes for which …

Constructive definitions of discrete random measures, which specify a sampling procedure
for the weights and atom locations of the measure, have proven to be of great value in …

We demonstrate a simple analytic argument that may be used to bound the Lévy
concentration function of a sum of independent random variables. The main application is a …

The limit theorems of probability theory are at the core of multiple models used in the broad
field of scientific research. Their main function is to replace the initial complicated stochastic …