On Comparison of the Estimators of the Hurst Index of the Solutions of Stochastic Differential Equations Driven by the Fractional Brownian Motion

Article type: Research Article

Authors: Kubilius, Kęstutis^; | Melichov, Dmitrij

Affiliations: Vilnius University Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania, E-mail: [email protected] | Vilnius Gediminas Technical University, Saulėtekio 11, LT-10223 Vilnius, Lithuania

Note: [] Supported by the Research Council of Lithuaniam contract No. MIP-66/2010.

Abstract: This paper presents a study of the Hurst index estimation in the case of fractional Ornstein–Uhlenbeck and geometric Brownian motion models. The performance of the estimators is studied both with respect to the value of the Hurst index and the length of sample paths.

Keywords: fractional Brownian motion, Hurst index, Ornstein–Uhlenbeck process, geometric Brownian motion

Journal: Informatica, vol. 22, no. 1, pp. 97-114, 2011