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

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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.

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Authors
  1. O. V. Shkol’nyi
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  2. M. V. Prats’ovytyi
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1653–1660, December, 1997.

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Shkol’nyi, O.V., Prats’ovytyi, M.V. One class of singular complex-valued random variables of the Jessen-Wintner type. Ukr Math J 49, 1862–1871 (1997). https://doi.org/10.1007/BF02513065

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  • DOI: https://doi.org/10.1007/BF02513065

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