On estimation of the Hurst index of solutions of stochastic integral equations - Kubilius, Kęstutis; Melichov, Dmitrij (Lietuvos matematikos rinkinys, 2008)
Let X be a solution of a stochasti Let X be a solution of a stochastic integral equation driven by a fractional Brownian motion BH and let Vn(X, 2) = \sumn k=1(\DeltakX)2, where \DeltakX = X( k+1/n ) - X(k/n ). We study the ditions n2H-1Vn(X, 2) convergence almost surely as n → ∞ holds. This fact is used to obtain a strongly consistent estimator of the Hurst index H, 1/2 < H < 1.
Keywords: fractional Brownian motion; quadratic variation; consistent estimator