Open AccessOn estimation of the Hurst index of solutions of stochastic integral equations
Author(s) -
Kęstutis Kubilius,
Dmitrij Melichov
Publication year - 2008
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2008.18148
Subject(s) - fractional brownian motion , estimator , mathematics , hurst exponent , index (typography) , convergence (economics) , brownian motion , integral equation , mathematical analysis , statistics , computer science , economics , economic growth , world wide web
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.