Quadratic variations and estimation of the hurst index of the solution of SDE driven by a fractional Brownian motion

Abstract

In this paper, we derive two strongly consistent Hurst index estimators from the limit behavior of the first-and second-order quadratic variations of the solution of an SDE driven by a fractional Brownian motion. We also show that these estimators retain their properties if the solution is replaced with its Milstein approximation.