Albeverio, S.; Ivanenko, Ganna; Lebid, Mykola; Torbin, Grygoriy On the Hausdorff dimension faithfulness and the Cantor series expansion. (English) Zbl 1488.28008 Methods Funct. Anal. Topol. 26, No. 4, 298-310 (2020). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 28A80 11K55 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Methods Funct. Anal. Topol. 26, No. 4, 298--310 (2020; Zbl 1488.28008) Full Text: DOI arXiv
Sydoruk, Liliia; Torbin, Grygoriy On singularity of distribution of random variables with independent symbols of Oppenheim expansions. (English) Zbl 1423.11137 Mod. Stoch., Theory Appl. 4, No. 3, 273-283 (2017). MSC: 11K55 60G30 PDFBibTeX XMLCite \textit{L. Sydoruk} and \textit{G. Torbin}, Mod. Stoch., Theory Appl. 4, No. 3, 273--283 (2017; Zbl 1423.11137) Full Text: DOI arXiv
Garko, I. I.; Nikiforov, R. O.; Torbin, G. M. On the \(G\)-isomorphism of probability and dimensional theories of representations of real numbers and fractal faithfulness of systems of coverings. (English. Ukrainian original) Zbl 1414.11096 Theory Probab. Math. Stat. 94, 17-36 (2017); translation from Teor. Jmovirn. Mat. Stat. 94, 16-35 (2016). MSC: 11K55 37B10 28A80 60G30 PDFBibTeX XMLCite \textit{I. I. Garko} et al., Theory Probab. Math. Stat. 94, 17--36 (2017; Zbl 1414.11096); translation from Teor. Jmovirn. Mat. Stat. 94, 16--35 (2016) Full Text: DOI
Albeverio, Sergio; Kondratiev, Yuri; Nikiforov, Roman; Torbin, Grygoriy On new fractal phenomena connected with infinite linear IFS. (English) Zbl 1426.11077 Math. Nachr. 290, No. 8-9, 1163-1176 (2017). MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Math. Nachr. 290, No. 8--9, 1163--1176 (2017; Zbl 1426.11077) Full Text: DOI arXiv
Albeverio, Sergio; Garko, Iryna; Ibragim, Muslem; Torbin, Grygoriy Non-normal numbers: full Hausdorff dimensionality vs zero dimensionality. (English. French summary) Zbl 1422.11164 Bull. Sci. Math. 141, No. 2, 1-19 (2017). Reviewer: Jan Šustek (Ostrava) MSC: 11K55 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Bull. Sci. Math. 141, No. 2, 1--19 (2017; Zbl 1422.11164) Full Text: DOI
Ibragim, Muslem; Torbin, Grygoriy On fractal faithfulness and fine fractal properties of random variables with independent \(Q^*\)-digits. (English) Zbl 1355.11081 Mod. Stoch., Theory Appl. 3, No. 2, 119-131 (2016). Reviewer: Tomas Persson (Lund) MSC: 11K55 26A30 28A80 60G30 PDFBibTeX XMLCite \textit{M. Ibragim} and \textit{G. Torbin}, Mod. Stoch., Theory Appl. 3, No. 2, 119--131 (2016; Zbl 1355.11081) Full Text: DOI arXiv
Ibragim, M. H.; Torbin, G. M. A probabilistic approach to studies of DP-transformations and faithfullness of covering systems to evaluate the Hausdorff-Besicovitch dimension. (English. Ukrainian original) Zbl 1346.60074 Theory Probab. Math. Stat. 92, 23-36 (2016); translation from Teor. Jmovirn. Mat. Stat. 92, 29-40 (2015). MSC: 60G99 60E99 60G30 28A78 28A80 11K55 PDFBibTeX XMLCite \textit{M. H. Ibragim} and \textit{G. M. Torbin}, Theory Probab. Math. Stat. 92, 23--36 (2016; Zbl 1346.60074); translation from Teor. Jmovirn. Mat. Stat. 92, 29--40 (2015) Full Text: DOI
Albeverio, Sergio; Kulyba, Yuliya; Pratsiovytyi, Mykola; Torbin, Grygoriy On singularity and fine spectral structure of random continued fractions. (English) Zbl 1377.11087 Math. Nachr. 288, No. 16, 1803-1813 (2015). MSC: 11K55 11J70 28A80 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Math. Nachr. 288, No. 16, 1803--1813 (2015; Zbl 1377.11087) Full Text: DOI
Kondratiev, Yuri; Lebid, Mykola; Slutskyi, Oleksandr; Torbin, Grygoriy Cantor series expansions and packing dimension faithfulness. arXiv:1507.05663 Preprint, arXiv:1507.05663 [math.MG] (2015). MSC: 11K55 28A78 28A80 11K55 28A78 28A80 60G30 BibTeX Cite \textit{Y. Kondratiev} et al., ``Cantor series expansions and packing dimension faithfulness'', Preprint, arXiv:1507.05663 [math.MG] (2015) Full Text: arXiv OA License
Albeverio, Sergio; Pratsiovyta, Iryna; Pratsiovytyi, Mykola; Torbin, Grygoriy On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties. arXiv:1506.04357 Preprint, arXiv:1506.04357 [math.PR] (2015). MSC: 11K55 26A30 28A80 60E10 BibTeX Cite \textit{S. Albeverio} et al., ``On Bernoulli convolutions generated by second Ostrogradsky series and their fine fractal properties'', Preprint, arXiv:1506.04357 [math.PR] (2015) Full Text: arXiv OA License
Albeverio, Sergio; Torbin, Gregory Ostrogradsky-Sierpiński-Pierce expansion: dynamical systems, probability theory and fractal geometry points of view. arXiv:1506.04355 Preprint, arXiv:1506.04355 [math.PR] (2015). MSC: 11K55 28A80 37A45 37B10 60G30 BibTeX Cite \textit{S. Albeverio} and \textit{G. Torbin}, ``Ostrogradsky-Sierpiński-Pierce expansion: dynamical systems, probability theory and fractal geometry points of view'', Preprint, arXiv:1506.04355 [math.PR] (2015) Full Text: arXiv OA License
Albeverio, Sergio; Pratsiovyta, Iryna; Torbin, Grygoriy On metric, dynamical, probabilistic and fractal phenomena connected with the second Ostrogradsky expansion. arXiv:1506.04353 Preprint, arXiv:1506.04353 [math.PR] (2015). MSC: 11K55 28A80 37A45 37B10 60G30 BibTeX Cite \textit{S. Albeverio} et al., ``On metric, dynamical, probabilistic and fractal phenomena connected with the second Ostrogradsky expansion'', Preprint, arXiv:1506.04353 [math.PR] (2015) Full Text: arXiv OA License
Lebid’, M. V.; Torbin, G. M. On comparable and non-comparable Hausdorff measures. (Ukrainian. English summary) Zbl 1313.60078 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2014, No. 8, 35-40 (2014). MSC: 60G30 11K55 28A80 PDFBibTeX XMLCite \textit{M. V. Lebid'} and \textit{G. M. Torbin}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2014, No. 8, 35--40 (2014; Zbl 1313.60078) Full Text: DOI OA License
Albeverio, Sergio; Kondratiev, Yuri; Nikiforov, Roman; Torbin, Grygoriy On fractal properties of non-normal numbers with respect to Rényi \(f\)-expansions generated by piecewise linear functions. (English) Zbl 1294.11133 Bull. Sci. Math. 138, No. 3, 440-455 (2014). Reviewer: Marius Iosifescu (Bucureşti) MSC: 11K55 28A80 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Bull. Sci. Math. 138, No. 3, 440--455 (2014; Zbl 1294.11133) Full Text: DOI
Lebid’, M. V.; Torbin, G. M. Singularity and fine fractal properties of a certain class of infinite Bernoulli convolutions with an essential intersection. (English. Ukrainian original) Zbl 1329.60107 Theory Probab. Math. Stat. 87, 99-115 (2013); translation from Teor. Jmovirn. Mat. Stat. 87, 89-104 (2012). MSC: 60G30 28A80 28A78 PDFBibTeX XMLCite \textit{M. V. Lebid'} and \textit{G. M. Torbin}, Theory Probab. Math. Stat. 87, 99--115 (2013; Zbl 1329.60107); translation from Teor. Jmovirn. Mat. Stat. 87, 89--104 (2012) Full Text: DOI
Nikiforov, R. O.; Torbin, G. M. Fractal properties of random variables with independent \(Q_\infty\)-symbols. (English. Ukrainian original) Zbl 1300.60055 Theory Probab. Math. Stat. 86, 169-182 (2013); translation from Teor. Jmovirn. Mat. Stat. 86, 150-162 (2012). MSC: 60G30 11K55 28A80 PDFBibTeX XMLCite \textit{R. O. Nikiforov} and \textit{G. M. Torbin}, Theory Probab. Math. Stat. 86, 169--182 (2013; Zbl 1300.60055); translation from Teor. Jmovirn. Mat. Stat. 86, 150--162 (2012) Full Text: DOI
Albeverio, S.; Koshmanenko, V.; Pratsiovytyi, M.; Torbin, G. On fine structure of singularly continuous probability measures and random variables with independent \(\tilde{Q}\)-symbols. (English) Zbl 1240.28019 Methods Funct. Anal. Topol. 17, No. 2, 97-111 (2011). Reviewer: A. N. Kochubei (Kyïv) MSC: 28A80 11K55 26A30 60G50 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Methods Funct. Anal. Topol. 17, No. 2, 97--111 (2011; Zbl 1240.28019)
Torbin, G. M.; Pratsyovyta, I. M. Singularity of the second Ostrogradskii random series. (Ukrainian, English) Zbl 1224.11070 Teor. Jmovirn. Mat. Stat. 81, 164-172 (2009); translation in Theory Probab. Math. Stat. 81, 187-195 (2010). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 11K55 60G30 37B10 37A50 PDFBibTeX XMLCite \textit{G. M. Torbin} and \textit{I. M. Pratsyovyta}, Teor. Ĭmovirn. Mat. Stat. 81, 164--172 (2009; Zbl 1224.11070); translation in Theory Probab. Math. Stat. 81, 187--195 (2010) Full Text: DOI
Albeverio, Sergio; Baranovskyi, Oleksandr; Pratsiovytyi, Mykola; Torbin, Grygoriy The set of incomplete sums of the first Ostrogradsky series and anomalously fractal probability distributions on it. (English) Zbl 1199.60036 Rev. Roum. Math. Pures Appl. 54, No. 2, 85-115 (2009). Reviewer: Cryssoula Ganatsiou (Larissa) MSC: 60E05 11K55 26A30 28A80 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Rev. Roum. Math. Pures Appl. 54, No. 2, 85--115 (2009; Zbl 1199.60036)
Torbin, Grygoriy; Pratsiovyta, Iryna On ergodic, metric and fractal properties of the second Ostrogradsky expansion of real numbers. (English) Zbl 1329.11081 Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 199-202 (2008). MSC: 11K55 11K50 PDFBibTeX XMLCite \textit{G. Torbin} and \textit{I. Pratsiovyta}, in: Voronoï's impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22--28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine. 199--202 (2008; Zbl 1329.11081)
Torbin, Grygoriy; Nikiforov, Roman; Kolesnik, Maksym Measure, topology and fractal geometry of non-normal numbers for expansions with infinite alphabets. (English) Zbl 1344.11055 Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 195-198 (2008). MSC: 11K55 28A80 PDFBibTeX XMLCite \textit{G. Torbin} et al., in: Voronoï's impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22--28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine. 195--198 (2008; Zbl 1344.11055)
Baranovskyi, Oleksandr; Pratsiovytyi, Mykola; Torbin, Grygoriy On Lebesgue measure and fractal dimension of sets related to the first Ostrogradsky expansion. (English) Zbl 1335.11065 Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 191-194 (2008). MSC: 11K55 11K50 PDFBibTeX XMLCite \textit{O. Baranovskyi} et al., in: Voronoï's impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22--28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine. 191--194 (2008; Zbl 1335.11065)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M. Fractal properties of some Bernoulli convolutions. (Ukrainian, English) Zbl 1224.60082 Teor. Jmovirn. Mat. Stat. 79, 34-49 (2008); translation in Theory Probab. Math. Stat. 79, 39-55 (2009). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 60G30 11K55 28A80 PDFBibTeX XMLCite \textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 79, 34--49 (2008; Zbl 1224.60082); translation in Theory Probab. Math. Stat. 79, 39--55 (2009) Full Text: DOI
Albeverio, Sergio; Koval, Vyacheslav; Pratsiovytyi, Mykola; Torbin, G. On classification of singular measures and fractal properties of quasi-self-affine measures in \(\mathbb R^2\). (English) Zbl 1174.28006 Random Oper. Stoch. Equ. 16, No. 2, 181-211 (2008). Reviewer: Rostyslav E. Yamnenko (Kyïv) MSC: 28A80 11K55 26A30 28A78 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Random Oper. Stoch. Equ. 16, No. 2, 181--211 (2008; Zbl 1174.28006) Full Text: DOI
Torbin, G. M. On \(DP\)-properties of fractal probability measures with independent \(Q\)-symbols. (Ukrainian. English summary) Zbl 1164.60305 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 4, 44-50 (2008). MSC: 60A10 PDFBibTeX XMLCite \textit{G. M. Torbin}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2008, No. 4, 44--50 (2008; Zbl 1164.60305)
Albeverio, Sergio; Torbin, Grygoriy On fine fractal properties of generalized infinite Bernoulli convolutions. (English) Zbl 1162.28002 Bull. Sci. Math. 132, No. 8, 711-727 (2008). Reviewer: Victoria Knopova (Kiev) MSC: 28A80 60G60 60G50 PDFBibTeX XMLCite \textit{S. Albeverio} and \textit{G. Torbin}, Bull. Sci. Math. 132, No. 8, 711--727 (2008; Zbl 1162.28002) Full Text: DOI arXiv
Albeverio, Sergio; Pratsiovytyi, Mykola; Torbin, Grygoriy Transformations preserving the Hausdorff-Besicovitch dimension. (English) Zbl 1134.28007 Cent. Eur. J. Math. 6, No. 1, 119-128 (2008). MSC: 28A80 11K55 28A78 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Cent. Eur. J. Math. 6, No. 1, 119--128 (2008; Zbl 1134.28007) Full Text: DOI
Torbin, Grygorij Probabilistic approach to transformations preserving the fractal dimension. (Ukrainian. English summary) Zbl 1174.28312 Mat. Visn. Nauk. Tov. Im. Shevchenka 4, 275-283 (2007). MSC: 28A80 60G30 11K55 28A78 PDFBibTeX XMLCite \textit{G. Torbin}, Mat. Visn. Nauk. Tov. Im. Shevchenka 4, 275--283 (2007; Zbl 1174.28312)
Torbin, Grygoriy Probability distributions with independent Q-symbols and transformations preserving the Hausdorff dimension. (English) Zbl 1142.60032 Theory Stoch. Process. 13, No. 29, Part 1-2, 281-293 (2007). Reviewer: A. D. Borisenko (Kyïv) MSC: 60G30 28A80 11K55 PDFBibTeX XMLCite \textit{G. Torbin}, Theory Stoch. Process. 13(29), No. 1--2, 281--293 (2007; Zbl 1142.60032)
Albeverio, S.; Goncharenko, Ya.; Pratsiovytyi, M.; Torbin, G. Convolutions of distributions of random variables with independent binary digits. (English) Zbl 1164.60004 Random Oper. Stoch. Equ. 15, No. 1, 89-104 (2007). Reviewer: Rostyslav E. Yamnenko (Kyïv) MSC: 60E10 11K55 28A80 30B20 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Random Oper. Stoch. Equ. 15, No. 1, 89--104 (2007; Zbl 1164.60004) Full Text: DOI
Albeverio, Sergio; Baranovskyi, Oleksandr; Pratsiovytyi, Mykola; Torbin, Grygoriy The Ostrogradsky series and related Cantor-like sets. (English) Zbl 1131.11052 Acta Arith. 130, No. 3, 215-230 (2007). Reviewer: Jean-Paul Allouche (Paris) MSC: 11K55 11K50 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Acta Arith. 130, No. 3, 215--230 (2007; Zbl 1131.11052) Full Text: DOI arXiv
Albeverio, Sergio; Gontcharenko, Yana; Pratsiovytyi, Mykola; Torbin, Grygoriy Jessen-Wintner type random variables and fractal properties of their distributions. (English) Zbl 1160.28002 Math. Nachr. 279, No. 15, 1619-1633 (2006). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 28A80 11K55 60E05 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Math. Nachr. 279, No. 15, 1619--1633 (2006; Zbl 1160.28002) Full Text: DOI
Albeverio, Sergio; Koshmanenko, Volodymyr; Pratsiovytyi, Mykola; Torbin, Grygoriy Spectral properties of image measures under the infinite conflict interaction. (English) Zbl 1196.28002 Positivity 10, No. 1, 39-49 (2006). MSC: 28A12 60G30 15B52 11A67 11K55 26A46 28A80 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Positivity 10, No. 1, 39--49 (2006; Zbl 1196.28002) Full Text: DOI arXiv Link
Torbin, G. M. Multi-fractal analysis of singular continuous probability measures. (Ukrainian, English) Zbl 1099.28006 Ukr. Mat. Zh. 57, No. 5, 706-721 (2005); translation in Ukr. Math. J. 57, No. 5, 837-857 (2005). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 28A80 26A30 28A78 PDFBibTeX XMLCite \textit{G. M. Torbin}, Ukr. Mat. Zh. 57, No. 5, 706--721 (2005; Zbl 1099.28006); translation in Ukr. Math. J. 57, No. 5, 837--857 (2005) Full Text: DOI
Albeverio, S.; Pratsiovytyi, M.; Torbin, G. Singular probability distributions and fractal properties of sets of real numbers defined by the asymptotic frequencies of their \(s\)-adic digits. (English) Zbl 1097.11038 Ukr. Mat. Zh. 57, No. 9, 1163-1170 (2005) and Ukr. Math. J. 57, No. 9, 1361-1370 (2005). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 11K55 28A80 54F50 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Ukr. Mat. Zh. 57, No. 9, 1163--1170 (2005; Zbl 1097.11038) Full Text: DOI arXiv
Albeverio, Sergio; Pratsiovytyi, Mykola; Torbin, Grygoriy Topological and fractal properties of real numbers which are not normal. (English) Zbl 1088.28003 Bull. Sci. Math. 129, No. 8, 615-630 (2005). MSC: 28A80 11K55 28A78 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Bull. Sci. Math. 129, No. 8, 615--630 (2005; Zbl 1088.28003) Full Text: DOI
Albeverio, Sergio; Torbin, Grygoriy Fractal properties of singular probability distributions with independent \(Q^{\ast}\)-digits. (English) Zbl 1082.11049 Bull. Sci. Math. 129, No. 4, 356-367 (2005). Reviewer: Cryssoula Ganatsiou (Larissa) MSC: 11K55 28A80 60G30 PDFBibTeX XMLCite \textit{S. Albeverio} and \textit{G. Torbin}, Bull. Sci. Math. 129, No. 4, 356--367 (2005; Zbl 1082.11049) Full Text: DOI
Albeverio, Sergio; Pratsiovytyi, Mykola; Torbin, Grygoriy Fractal probability distributions and transformations preserving the Hausdorff-Besicovitch dimension. (English) Zbl 1115.37016 Ergodic Theory Dyn. Syst. 24, No. 1, 1-16 (2004). MSC: 37C45 11K55 28A78 60E05 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Ergodic Theory Dyn. Syst. 24, No. 1, 1--16 (2004; Zbl 1115.37016) Full Text: DOI
Prats’ovytyj, M. V.; Torbin, G. M. Fractal geometry and transformations preserving the Hausdorff-Besicovitch dimension. (Ukrainian) Zbl 1098.60003 Ukrainian mathematical congress – 2001, Kiev, Ukraine, August 21–23, 2001. Proceedings. Section 2. Dynamical analysis. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 966-02-3009-5). 77-93 (2003). MSC: 60A10 28A78 60E05 28A80 PDFBibTeX XMLCite \textit{M. V. Prats'ovytyj} and \textit{G. M. Torbin}, in: Ukraïns'kyj matematychnyj kongres -- 2001. Pratsi. Sektsiya 2. Dynamichni systemy. Kyïv: Instytut Matematyky NAN Ukraïny. 77--93 (2003; Zbl 1098.60003)
Albeverio, Sergio; Koshmanenko, Volodymyr; Torbin, Grygoriy Fine structure of the singular continuous spectrum. (English) Zbl 1024.28003 Methods Funct. Anal. Topol. 9, No. 2, 101-119 (2003). Reviewer: A.N.Kochubei (Kyïv) MSC: 28A12 26A30 28A50 28A80 47B25 47A10 PDFBibTeX XMLCite \textit{S. Albeverio} et al., Methods Funct. Anal. Topol. 9, No. 2, 101--119 (2003; Zbl 1024.28003)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M. Topological metric and fractal properties of the convolution of two singular distributions with independent binary digits. (Ukrainian, English) Zbl 1051.60013 Teor. Jmovirn. Mat. Stat. 67, 9-19 (2002); translation in Theory Probab. Math. Stat. 67, 11-22 (2003). Reviewer: N. M. Zinchenko (Kyïv) MSC: 60E05 28A80 PDFBibTeX XMLCite \textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 67, 9--19 (2002; Zbl 1051.60013); translation in Theory Probab. Math. Stat. 67, 11--22 (2003)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M. Fractal properties of the set of points of non-differentiability of absolutely continuous and singular distribution functions. (Ukrainian, English) Zbl 1027.60005 Teor. Jmovirn. Mat. Stat. 65, 25-32 (2000); translation in Theory Probab. Math. Stat. 65, 27-35 (2002). Reviewer: Mikhail Moklyachuk (Kyïv) MSC: 60E05 28A80 PDFBibTeX XMLCite \textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 65, 25--32 (2000; Zbl 1027.60005); translation in Theory Probab. Math. Stat. 65, 27--35 (2002)
Prats’ovytyj, M. V.; Torbin, G. M. A class of random variables of the Jessen-Wintner type. (Ukrainian) Zbl 0940.60041 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 4, 48-54 (1998). MSC: 60F99 PDFBibTeX XMLCite \textit{M. V. Prats'ovytyj} and \textit{G. M. Torbin}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 4, 48--54 (1998; Zbl 0940.60041)
Prats’ovytyj, M. V.; Torbin, G. M. Superfractality of the set of numbers having no frequency of \(n\)-adic digits and fractal probability distributions. (English. Ukrainian original) Zbl 0936.28002 Ukr. Math. J. 47, No. 7, 1113-1118 (1995); translation from Ukr. Mat. Zh. 47, No. 7, 971-975 (1995). Reviewer: M.P.Moklyachuk (Kyïv) MSC: 28A80 28A78 30B20 60D05 PDFBibTeX XMLCite \textit{M. V. Prats'ovytyj} and \textit{G. M. Torbin}, Ukr. Mat. Zh. 47, No. 7, 971--975 (1995; Zbl 0936.28002); translation from Ukr. Mat. Zh. 47, No. 7, 971--975 (1995)