Kurchenko, O. O. One strong consistency estimate of the Hurst parameter of the fractional Brownian motion. (Ukrainian, English) Zbl 1050.60035 Teor. Jmovirn. Mat. Stat. 67, 88-96 (2002); translation in Theory Probab. Math. Stat. 67, 97-106 (2003). A Lévy-Baxter type theorem for the fractional Brownian motion with Hurst parameter \(H\in (0,1)\) is proved. Then an estimate of \(H\) is constructed on the basis of Baxter type statistics. The strong consistency of the proposed statistics is proved, and the rate of their a.s. convergence is investigated. Reviewer: N. M. Zinchenko (Kyïv) Cited in 3 Documents MSC: 60F15 Strong limit theorems 60J65 Brownian motion 60G15 Gaussian processes Keywords:fractional Brownian motion; Lévy-Baxter theorem; Hurst parameter; strong consistency estimate PDFBibTeX XMLCite \textit{O. O. Kurchenko}, Teor. Ĭmovirn. Mat. Stat. 67, 88--96 (2002; Zbl 1050.60035); translation in Theory Probab. Math. Stat. 67, 97--106 (2003)