2019
Том 71
№ 8

All Issues

O. V. Shkol’nyi

Articles: 2
Brief Communications (Ukrainian)

Random variables determined by the distributions of their digits in a numeration system with complex base

O. V. Shkol’nyi

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 12. - pp. 1715–1720

We study the distributions of complex-valued random variables determined by the distributions of their digits in a numeration system with complex base. We establish sufficient conditions for the singularity of such random variables, in particular, in the cases where their spectrum has Lebesgue measure zero (C-type singular distribution) or is a rectangle (S-type singular distribution).

Article (Ukrainian)

One class of singular complex-valued random variables of the Jessen-Wintner type

O. V. Shkol’nyi, Pratsiovytyi M. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1653–1660

We study the structure of the distribution of a complex-valued random variable ξ = Σa k ξ k , where ξ k are independent complex-valued random variables with discrete distribution and a k are terms of an absolutely convergent series. We establish a criterion of discreteness and sufficient conditions for singularity of the distribution of ξ and investigate the fractal properties of the spectrum.