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Asymptotic properties of non-standard drift parameter estimators in the models involving fractional Brownian motion


Authors: Meriem Bel Hadj Khlifa, Yuliya Mishura and Mounir Zili
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 94 (2016).
Journal: Theor. Probability and Math. Statist. 94 (2017), 77-88
MSC (2010): Primary 62F10, 62F12; Secondary 60G22
DOI: https://doi.org/10.1090/tpms/1010
Published electronically: August 25, 2017
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Abstract: We investigate the problem of estimation of the unknown drift parameter in the stochastic differential equations driven by fractional Brownian motion, with the coefficients supplying standard existence-uniqueness demands. We consider a particular case when the ratio of drift and diffusion coefficients is non-random, and establish the asymptotic strong consistency of the estimator with different ratios, from many classes of non-random standard functions. Simulations are provided to illustrate our results, and they demonstrate the fast rate of convergence of the estimator to the true value of a parameter.


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Additional Information

Meriem Bel Hadj Khlifa
Affiliation: Faculty of Sciences of Monastir, Department of Mathematics, Avenue de l’Environnement, 5000, Monastir, Tunisia
Email: meriem.bhk17121988@outlook.fr

Yuliya Mishura
Affiliation: Department of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Street, 64, 01601 Kyiv, Ukraine
Email: myus@univ.kiev.ua

Mounir Zili
Affiliation: Faculty of Sciences of Monastir, Department of Mathematics, Avenue de l’Environnement, 5000, Monastir, Tunisia
Email: Mounir.Zili@fsm.rnu.tn

DOI: https://doi.org/10.1090/tpms/1010
Keywords: Parameter estimators, fractional Brownian motion, strong consistency, estimation of fractional derivatives
Received by editor(s): March 17, 2016
Published electronically: August 25, 2017
Article copyright: © Copyright 2017 American Mathematical Society