Properties of maximum likelihood estimates in diffusion and fractional-Brownian models
Author:
Nadiya Rudomino-Dusyats’ka
Translated by:
Yu. Mishura
Journal:
Theor. Probability and Math. Statist. 68 (2004), 139-146
MSC (2000):
Primary 60H10, 62F12
DOI:
https://doi.org/10.1090/S0094-9000-04-00600-3
Published electronically:
May 24, 2004
MathSciNet review:
2000643
Full-text PDF Free Access
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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.
References
- M. Zähle, Integration with respect to fractional functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), 333–374. MR 99j:60073
- Yu. Mishura and N. Rudomino-Dusyatska, Consistency of drift parameter estimates in fractional Brownian diffusion models, Theory Stoch. Processes 7\rom(23\rom) (2001), no. 3–4, 103–112.
- A. Kukush, Yu. Mishura, and E. Valkeila, Statistical Inference with Fractional Brownian Motion, Preprint, Turku University, 2001.
- L. Decreusefond and A. S. Üstünel, Stochastic analysis on fractional Brownian motion, Potential Analysis 10 (1998), 177–214. MR 2000b:60133
- I. A. Ibragimov and R. Z. Khas’minskiĭ, Statistical Estimation: Asymptotic Theory, “Nauka", Moscow, 1979; English transl., Springer-Verlag, Berlin–Heidelberg–New York, 1981. MR 81h:62004
References
- M. Zähle, Integration with respect to fractional functions and stochastic calculus. I, Probab. Theory Related Fields 111 (1998), 333–374. MR 99j:60073
- Yu. Mishura and N. Rudomino-Dusyatska, Consistency of drift parameter estimates in fractional Brownian diffusion models, Theory Stoch. Processes 7\rom(23\rom) (2001), no. 3–4, 103–112.
- A. Kukush, Yu. Mishura, and E. Valkeila, Statistical Inference with Fractional Brownian Motion, Preprint, Turku University, 2001.
- L. Decreusefond and A. S. Üstünel, Stochastic analysis on fractional Brownian motion, Potential Analysis 10 (1998), 177–214. MR 2000b:60133
- I. A. Ibragimov and R. Z. Khas’minskiĭ, Statistical Estimation: Asymptotic Theory, “Nauka", Moscow, 1979; English transl., Springer-Verlag, Berlin–Heidelberg–New York, 1981. MR 81h:62004
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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
Email:
nadiya_rudomino@hotmail.com
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
