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

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.