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

Abstract

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.