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Asymptotic behavior of mixed power variations and statistical estimation in mixed models

  • Marco Dozzi
  • Yuliya Mishura
  • Georgiy Shevchenko
Article

Abstract

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.

Keywords

Power variation Fractional Brownian motion Hurst parameter Wiener process Consistent estimator 

Mathematics Subject Classification

60G22 62M09 60G15 62F25 

Notes

Acknowledgments

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.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Marco Dozzi
    • 1
  • Yuliya Mishura
    • 2
  • Georgiy Shevchenko
    • 2
  1. 1.Institut Elie CartanUniversité de LorraineVandoeuvre-les-Nancy CedexFrance
  2. 2.Department of Probability Theory, Statistics and Actuarial MathematicsTaras Shevchenko National University of KyivKyivUkraine

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