2018
Том 70
№ 7

All Issues

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

Litvinyuk A. A.

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Abstract

By using the method of characteristic functions, we obtain sufficient conditions for the singularity of a random variable. $$ξ = \sum_{k=1}^{∞} 2^{−k}ξ_k,$$ where $ξ_k$ are independent identically distributed random variables taking values $x_0, x_1$, and $x_2$ $(x_0 < x_1 < x_2)$ with probabilities $p_0, p_1$ and $p_2$, respectively, such that $p_i ≥ 0,\; p_0 + p_1 + p_2 = 1$ and $2(x_1 − x_0)/(x_2−x_0)$ is a rational number.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 1, pp 140-145.

Citation Example: Litvinyuk A. A. On types of distributions of sums of one class of random power series with independent identically distributed coefficients // Ukr. Mat. Zh. - 1999. - 51, № 1. - pp. 128–132.

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