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On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

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Abstract

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions.

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Authors and Affiliations

  1. National Pedagogic University, Kiev

    N. V. Pratsevityi

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  1. N. V. Pratsevityi
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998.

The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant No. APU 061086).

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Pratsevityi, N.V. On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem. Ukr Math J 50, 1233–1241 (1998). https://doi.org/10.1007/BF02513095

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  • DOI: https://doi.org/10.1007/BF02513095

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