2019
Том 71
№ 8

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

Litvinyuk A. A.

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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