Asymptotic behavior of mixed power variations and statistical estimation in mixed models
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We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter estimators in mixed models.
KeywordsPower variation Fractional Brownian motion Hurst parameter Wiener process Consistent estimator
Mathematics Subject Classification60G22 62M09 60G15 62F25
This work has been partially supported by the Commission of the European Committees Grant PIRSES-GA-2008-230804 within the program “Marie Curie Actions”. The authors are also grateful to Rim Touibi and anonymous referees for their careful reading of the manuscript and helpful suggestions, which helped to improve the article.
- Benassi A., Deguy S (1999) Multi-scale fractional Brownian motion: definition and identification. Preprint LAICGoogle Scholar
- Cai, C, Chigansky P, Kleptsyna M (2012) ‘The maximum likelihood drift estimator for mixed fractional Brownian motion’. Preprint, available online at http://arxiv.org/abs/1208.6253
- Coeurjolly J-F (2000) Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study. J Stat Softw 5:1–53Google Scholar
- Filatova D (2008) Mixed fractional Brownian motion: some related questions for computer network traffic modeling. International conference on signals and electronic systems, Kraków 2008, pp 393–396Google Scholar
- Kozachenko Y, Melnikov A, Mishura Y (2012) ‘On drift parameter estimation in models with fractional Brownian motion’. Statistics. To appear, available online at http://arxiv.org/abs/1112.2330
- Mishura YS (2008) Stochastic calculus for fractional Brownian motion and related processes, Vol. (1929) of Lecture Notes in Mathematics. Springer-Verlag, BerlinGoogle Scholar