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math.PR2026
Fractal random variables defined by probability distributions of digits of their -representation having two bases with different signs
M. Pratsiovytyi, O. Baranovskyi, I. Lysenko +1
In this paper, we study distributions of two random variables \begin{gather*} Ï= Ï_1 g_{1-Ï_1} + \sum_{k=2}^\infty Ï_k g_{1-Ï_k} \prod_{i=1}^{k-1} g_{Ï_i} \equiv Î^{G_2}_{Ï…
math.PR2026
Infinite Bernoulli convolutions generated by multigeometric series and their properties
Mykola Pratsiovytyi, Dmytro Karvatskyi, Oleg Makarchuk
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even int…
math.PR2026
Singular distributions of random variables with independent digits of representation in numeral system with natural base and redundant alphabet
Mykola Pratsiovytyi, Sofiia Ratushniak
Given natural parameters s and r, where , we consider the distribution of a random variable $ξ=\sum\limits_{k=1}^{\infty}s^{-k}ξ_k\equivÎ^{r_s}_{ξ_1ξ_2...ξ_k..…