$\widetilde{Q}$-representation of real numbers and fractal probability distributions
| dc.creator | Albeverio, Sergio | |
| dc.creator | Koshmanenko, Volodymyr | |
| dc.creator | Pratsiovytyi, Mykola | |
| dc.creator | Torbin, Grygoriy | |
| dc.date | 2003-08-01 | |
| dc.date | 2007-06-04 | |
| dc.date.accessioned | 2026-07-07T08:06:10Z | |
| dc.date.available | 2026-07-07T08:06:10Z | |
| dc.description | A $\widetilde{Q}-$representation of real numbers is introduced as a generalization of the $p-$adic and $Q-$representations. It is shown that the $\widetilde{Q}-$representation may be used as a convenient tool for the construction and study of fractals and sets with complicated local structure. Distributions of random variables $ξ$ with independent $\widetilde{Q}-$symbols are studied in details. Necessary and sufficient conditions for the probability measures $μ_ξ$ associated with $ξ$ to be either absolutely continuous or singular (resp. pure continuous, or pure point) are found in terms of the $\widetilde{Q}-$representation. In addition the metric-topological properties for the distribution of $ξ$ are investigated. A number of examples are presented. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0308007 | |
| dc.identifier | http://arxiv.org/abs/math/0308007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130512 | |
| dc.subject | Probability | |
| dc.subject | Number Theory | |
| dc.subject | 60G30; 11K55 | |
| dc.title | $\widetilde{Q}$-representation of real numbers and fractal probability distributions | |
| dc.type | text |