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Theory of Probability and Mathematical Statistics

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Properties of maximum likelihood estimates in diffusion and fractional-Brownian models

Author: Nadiya Rudomino-Dusyats'ka
Translated by: Yu. Mishura
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 68 (2003).
Journal: Theor. Probability and Math. Statist. 68 (2004), 139-146
MSC (2000): Primary 60H10, 62F12
Published electronically: May 24, 2004
MathSciNet review: 2000643
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Abstract: A mixed Brownian-fractional-Brownian model is considered. Two estimates for the shift parameter are constructed and compared. The local asymptotic normality and asymptotic efficiency of the estimates are established for the pure linear Brownian and fractional-Brownian models.

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Additional Information

Nadiya Rudomino-Dusyats'ka
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv–127 03127, Ukraine

Keywords: Fractional Brownian motion, Wiener process, diffusion model, Girsanov theorem, likelihood ratio
Received by editor(s): June 20, 2002
Published electronically: May 24, 2004
Article copyright: © Copyright 2004 American Mathematical Society