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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Asymptotic properties of an estimator for the drift coefficient of a stochastic differential equation with fractional Brownian motion


Authors: E. I. Kasyts'ka and P. S. Knopov
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 73-81
MSC (2000): Primary 60H10; Secondary 62M05
Published electronically: December 29, 2009
MathSciNet review: 2494536
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Abstract: A stochastic differential equation with respect to fractional Brownian motion is considered. We study the maximum likelihood estimator for the drift coefficient. We assume that the coefficient belongs to a given compact set of functions and prove the strong consistency of the estimator and its asymptotic normality.


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Additional Information

E. I. Kasyts'ka
Affiliation: Glushkov Institute for Cybernetics, National Academy of Sciences of Ukraine, Academician Glushkov Avenue, 03187 Kyiv, Ukraine

P. S. Knopov
Affiliation: Glushkov Institute for Cybernetics, National Academy of Sciences of Ukraine, Academician Glushkov Avenue, 03187 Kyiv, Ukraine
Email: knopov1@yahoo.com

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00781-9
PII: S 0094-9000(09)00781-9
Keywords: Fractional Wiener process, stochastic integral, stochastic differential equation, drift coefficient
Received by editor(s): July 7, 2008
Published electronically: December 29, 2009
Article copyright: © Copyright 2009 American Mathematical Society