On estimation of the Hurst index of solutions of stochastic integral equations | Zendy

Kęstutis Kubilius | Zendy; Dmitrij Melichov | Zendy

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On 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.

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