On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties
Abstract
Abstract We study properties of Bernoulli convolutions generated by the second Ostrogradsky series, i.e., probability distributions of random variables ξ = ∑ k = 1 ∞ ( - 1 ) k + 1 ξ k q k , see text \xi=\sum_{k=1}^{\infty}\frac{(-1)^{k+1}\xi_{k}}{q_{k}}, where q k {q_{k}} is a sequence of positive integers with q k + 1 ≥ q k ( q k + 1 ) {q_{k+1}\geq q_{k}(q_{k}+1)} , and { ξ k } {\{\xi_{k}\}} are independent random variables taking the values 0 and 1 with probabilities p 0 k {p_{0k}} and p 1 k {p_{1k}} respectively. We prove that ξ has an anomalously fractal Cantor-type singular distribution ( dim H ( S ξ ) = 0 {\dim_{H}(S_{\xi})=0}
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Random Operators and Stochastic Equations
- Publisher
- Walter de Gruyter GmbH
- Volume
- 34
- Issue
- 3
- Pages
- 243–263
- Publication date
- 25 August 2026
- Language
- EN