On estimation of the Hurst index of solutions of stochastic integral equations
Articles
Kęstutis Kubilius
Institute of Mathematics and Informatics
Dmitrij Melichov
Vilnius Gediminas Technical University
Published 2008-12-21
https://doi.org/10.15388/LMR.2008.18148
PDF

Keywords

fractional Brownian motion
quadratic variation
consistent estimator

How to Cite

Kubilius K. and Melichov D. (2008) “On estimation of the Hurst index of solutions of stochastic integral equations”, Lietuvos matematikos rinkinys, 48(proc. LMS), pp. 401–406. doi: 10.15388/LMR.2008.18148.

Abstract

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.

 

PDF
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please read the Copyright Notice in Journal Policy