Banna, Oksana; Buryak, Filipp; Mishura, Yuliya Distance from fractional Brownian motion with associated Hurst index \(0<H<1/2\) to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent. (English) Zbl 1468.60046 Mod. Stoch., Theory Appl. 7, No. 2, 191-202 (2020). Reviewer: B. L. S. Prakasa Rao (Hyderabad) MSC: 60G22 PDFBibTeX XMLCite \textit{O. Banna} et al., Mod. Stoch., Theory Appl. 7, No. 2, 191--202 (2020; Zbl 1468.60046) Full Text: DOI arXiv
Banna, Oksana; Mishura, Yuliya; Ralchenko, Kostiantyn; Shklyar, Sergiy Fractional Brownian motion. Approximations and projections. (English) Zbl 1506.60001 Mathematics and Statistics Series. London: ISTE; Hoboken, NJ: John Wiley & Sons (ISBN 978-1-78630-260-1/hbk). xvi, 266 p. (2019). Reviewer: B. L. S. Prakasa Rao (Hyderabad) MSC: 60-01 60G22 PDFBibTeX XMLCite \textit{O. Banna} et al., Fractional Brownian motion. Approximations and projections. London: ISTE; Hoboken, NJ: John Wiley \& Sons (2019; Zbl 1506.60001)
Banna, O. L.; Mishura, Yu. S.; Shklyar, S. V. Approximation of a Wiener process by integrals with respect to the fractional Brownian motion of power functions of a given exponent. (English. Ukrainian original) Zbl 1326.60076 Theory Probab. Math. Stat. 90, 13-22 (2015); translation from Teor. Jmovirn. Mat. Stat. 90, 13–21 (2014). MSC: 60H05 60G22 60G15 60G44 PDFBibTeX XMLCite \textit{O. L. Banna} et al., Theory Probab. Math. Stat. 90, 13--22 (2015; Zbl 1326.60076); translation from Teor. Jmovirn. Mat. Stat. 90, 13--21 (2014) Full Text: DOI
Shklyar, Sergiy; Shevchenko, Georgiy; Mishura, Yuliya; Doroshenko, Vadym; Banna, Oksana Approximation of fractional Brownian motion by martingales. (English) Zbl 1312.60043 Methodol. Comput. Appl. Probab. 16, No. 3, 539-560 (2014). MSC: 60G22 60G44 90C25 PDFBibTeX XMLCite \textit{S. Shklyar} et al., Methodol. Comput. Appl. Probab. 16, No. 3, 539--560 (2014; Zbl 1312.60043) Full Text: DOI arXiv
Mishura, Yu. S.; Banna, O. L.; Doroshenko, V. V. Distance of fractional Brownian motion to the subspaces of Gaussian martingales. (English) Zbl 1289.60073 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2013, No. 1, 53-60 (2013). MSC: 60G22 60G44 PDFBibTeX XMLCite \textit{Yu. S. Mishura} et al., Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2013, No. 1, 53--60 (2013; Zbl 1289.60073)
Mishura, Yu. S.; Banna, O. L. Fractional Brownian motion as limit of the Markov processes. (English) Zbl 1289.60072 Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2012, No. 4, 32-35 (2012). MSC: 60G22 60J25 PDFBibTeX XMLCite \textit{Yu. S. Mishura} and \textit{O. L. Banna}, Visn., Ser. Fiz.-Mat. Nauky, Kyïv. Univ. Im. Tarasa Shevchenka 2012, No. 4, 32--35 (2012; Zbl 1289.60072)
Banna, O. L.; Mishura, Yu. S. A bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval. (English. Russian original) Zbl 1243.60034 Theory Probab. Math. Stat. 83, 13-25 (2011); translation from Teor. Jmovirn. Mat. Stat. 83, 12-21 (2010). MSC: 60G15 60G44 60G22 60E15 PDFBibTeX XMLCite \textit{O. L. Banna} and \textit{Yu. S. Mishura}, Theory Probab. Math. Stat. 83, 13--25 (2011; Zbl 1243.60034); translation from Teor. Jmovirn. Mat. Stat. 83, 12--21 (2010) Full Text: DOI
Mishura, Yu. S.; Banna, O. L. Approximation of fractional Brownian motion by Wiener integrals. (Ukrainian, English) Zbl 1224.60079 Teor. Jmovirn. Mat. Stat. 79, 96-106 (2008); translation in Theory Probab. Math. Stat. 79, 107-116 (2009). Reviewer: Mikhail P. Moklyachuk (Kyïv) MSC: 60G22 60G44 PDFBibTeX XMLCite \textit{Yu. S. Mishura} and \textit{O. L. Banna}, Teor. Ĭmovirn. Mat. Stat. 79, 96--106 (2008; Zbl 1224.60079); translation in Theory Probab. Math. Stat. 79, 107--116 (2009) Full Text: DOI
Banna, Oksana L.; Mishura, Yuliya S. Approximation of fractional Brownian motion with associated Hurst index separated from 1 by stochastic integrals of linear power functions. (English) Zbl 1224.60074 Theory Stoch. Process. 14, No. 3-4, 1-16 (2008). Reviewer: A. D. Borisenko (Kyïv) MSC: 60G15 60H05 PDFBibTeX XMLCite \textit{O. L. Banna} and \textit{Y. S. Mishura}, Theory Stoch. Process. 14, No. 3--4, 1--16 (2008; Zbl 1224.60074)
Banna, O. L. Approximation of fractional Brownian motion having Hurst index close to one with stochastic integrals from linear-exponential integrand functions. (Ukrainian. English summary) Zbl 1164.60412 Prykl. Stat., Aktuarna Finans. Mat. 2007, No. 1, 60-67 (2007). MSC: 60J65 62P05 PDFBibTeX XMLCite \textit{O. L. Banna}, Prykl. Stat., Aktuarna Finans. Mat. 2007, No. 1, 60--67 (2007; Zbl 1164.60412)