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

• Date: 1999
• Main Authors: Litvinyuk, A. A., Литвинюк, А. А.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1999
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4591
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...