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Original Articles

Estimation of the Hurst parameter in some fractional processes

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Pages 542-554 | Received 09 May 2011, Accepted 13 Sep 2011, Published online: 18 Oct 2011

References

  • Davies , R. B. and Harte , D. S. 1987 . Tests for Hurst effect . Biometrika , 74 : 95 – 101 . (doi:10.1093/biomet/74.1.95)
  • Dieker , A. B. “ Simulation of fractional Brownian motion ” . Masters thesis, Vrije Universiteit, Amsterdam, 2002. Available at http://www2.isye.gatech.edu/adieker3/fbm/index.html
  • Bardet , J. M. , Lang , G. , Oppenheim , G. , Philippe , A. and Taqqu , M. S. 2003 . “ Generators of long-range dependent processes: A survey ” . In Theory and Applications of Long-Range Dependence , Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M. S. 579 – 623 . Boston , MA : Birkhäuser .
  • Cheridito , P. , Kawaguchi , H. and Maejima , M. 2003 . Fractional Ornstein–Uhlenbeck processes . Electron. J. Probab , 8 ( 3 ) : 14 (electronic)
  • Salminen , P. and Kaarakka , T. “ On fractional Ornstein–Uhlenbeck processes ” . preprint (2007). Available at http://arxiv.org/
  • Bogachev , V. I. 1998 . “ Gaussian Measures ” . Vol. 62 , xii – 433 . Providence , RI : American Mathematical Society (AMS) . Translated from the Russian by the author, Mathematical Surveys and Monographs
  • Rosenblatt , M. 1963 . Some results on the asymptotic behavior of eigenvalues for a class of integral equations with translation kernels . J. Math. Mech , 12 : 619 – 628 .
  • Widom , H. 1964 . Asymptotic behavior of the eigenvalues of certain integral equations. II . Arch. Ration. Mech. Anal , 17 : 215 – 229 . (doi:10.1007/BF00282438)
  • Bronski , J. C. 2003 . Small ball constants and tight eigenvalue asymptotics for fractional Brownian motions . J. Theoret. Probab , 16 : 87 – 100 . (doi:10.1023/A:1022226420564)
  • Bronski , J. C. 2003 . Asymptotics of Karhunen–Loève eigenvalues and tight constants for probability distributions of passive scalar transport . Comm. Math. Phys , 238 : 563 – 582 . (doi:10.1007/s00220-003-0835-3)
  • Yan , L. , Lu , Y. and Xu , Z. 2008 . Some properties of the fractional Ornstein–Uhlenbeck process . J. Phys. A , 41 : 145007.1 – 145007.17 . (doi:10.1088/1751-8113/41/14/145007)

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