Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift

Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it...

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Bibliographic Details
Published inNonlinear analysis (Vilnius, Lithuania) Vol. 25; no. 6; pp. 1059 - 1078
Main Author Kubilius, Kęstutis
Format Journal Article
LanguageEnglish
Published Vilnius University Press 01.11.2020
Subjects
backward Euler approximation
fractional Ait-Sahalia model
fractional Brownian motion
fractional CKLS model
Hurst index
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Summary:Strongly consistent and asymptotically normal estimates of the Hurst index H are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.
ISSN:1392-5113
2335-8963
DOI:10.15388/namc.2020.25.20565