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On types of distributions of sums of one class of random power series with independent identically distributed coefficients

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Abstract

By using the method of characteristic functions, we obtain sufficient conditions for the singularity of a random variable.

$$\xi = \sum\limits_{k = 1}^\infty {2^{ - k} \xi _k } $$

where ξ k are independent identically distributed random variables taking valuesx 0,x 1, andx 2 (x 0<x 1<x 2) with probabilitiesp 0,p 1 andp 2, respectively, such thatp i≥0,p 0+p 1+p 2 =1 and 2(x 1−x 0)/(x 2−x 0) is a rational number.

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Authors
  1. A. A. Litvinyuk
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Additional information

Pedagogic University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 128–132, January, 1999.

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Litvinyuk, A.A. On types of distributions of sums of one class of random power series with independent identically distributed coefficients. Ukr Math J 51, 140–145 (1999). https://doi.org/10.1007/BF02591923

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  • DOI: https://doi.org/10.1007/BF02591923

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