{"paper":{"title":"On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Grygoriy Torbin, Iryna Pratsiovyta, Mykola Pratsiovytyi, Sergio Albeverio","submitted_at":"2015-06-14T06:59:06Z","abstract_excerpt":"We study properties of Bernoulli convolutions generated by the second Ostrogradsky series, i.e., probability distributions of random variables \\begin{equation} \\xi = \\sum_{k=1}^\\infty \\frac{(-1)^{k+1}\\xi_k}{q_k}, \\end{equation} where $q_k$ is a sequence of positive integers with $q_{k+1}\\geq q_k(q_k+1)$, and $\\{\\xi_k\\}$ are independent random variables taking the values $0$ and $1$ with probabilities $p_{0k}$ and $p_{1k}$ respectively. We prove that $\\xi$ has an anomalously fractal Cantor type singular distribution ($\\dim_H (S_{\\xi})=0$) whose Fourier-Stieltjes transform does not tend to zero "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04357","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}