Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift
Articles
Kęstutis Kubilius
Vilnius University
https://orcid.org/0000-0002-1195-4243
Published 2020-11-01
https://doi.org/10.15388/namc.2020.25.20565
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Keywords

fractional Brownian motion
Hurst index
backward Euler approximation
fractional Ait-Sahalia model
fractional CKLS model

How to Cite

Kubilius K. (2020) “Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift”, Nonlinear Analysis: Modelling and Control, 25(6), pp. 1059-1078. doi: 10.15388/namc.2020.25.20565.

Abstract

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.

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