3 citations · 5 across the 8 of their papers we have counts for
7 papers · 1 filter
On singularity of distribution of random variables with independent symbols of Oppenheim expansions
Liliia Sinelnyk, Grygoriy Torbin
The paper is devoted to restricted Oppenheim expansion of real numbers (),which includes as partial cases already known Engel, Silvester and Lüroth expansions. We find conditi…
On fractal faithfulness and fine fractal properties of random variables with independent -digits
Muslem Ibragim, Grygoriy Torbin
We develop a new technique to prove the faithfulness of the Hausdorff--Besicovitch dimension calculation of the family of cylinders generated by -expansion of r…
On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties
Sergio Albeverio, Iryna Pratsiovyta, Mykola Pratsiovytyi +1
We study properties of Bernoulli convolutions generated by the second Ostrogradsky series, i.e., probability distributions of random variables \begin{equation} ξ= \sum_{k=1}^\infty…
Ostrogradsky-Sierpiński-Pierce expansion: dynamical systems, probability theory and fractal geometry points of view
Sergio Albeverio, Gregory Torbin
We establish several new probabilistic, dynamical, dimensional and number theoretical phenomena connected with Ostrogradsky-Sierpiński-Pierce expansion. First of all, we develop me…
On metric, dynamical, probabilistic and fractal phenomena connected with the second Ostrogradsky expansion
Sergio Albeverio, Iryna Pratsiovyta, Grygoriy Torbin
We consider the second Ostrogradsky expansion from the number theory, probability theory, dynamical systems and fractal geometry points of view, and establish several new phenomena…
On the Hausdorff dimension faithfulness and the Cantor series expansion
Sergio Albeverio, Ganna Ivanenko, Mykola Lebid +1
We study families of coverings which are faithful for the Hausdorff dimension calculation on a given set (i. e., special relatively narrow families of coverings leading to…