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

  • A. A. Litvinyuk


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.
How to Cite
Litvinyuk, A. A. “On Types of Distributions of Sums of One Class of Random Power Series With Independent Identically Distributed Coefficients”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 1, Jan. 1999, pp. 128–132, https://umj.imath.kiev.ua/index.php/umj/article/view/4591.
Short communications