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Sequential Analysis
Design Methods and Applications
Volume 23, 2004 - Issue 1
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Original Articles

Sequential Estimation for Fractional Ornstein–Uhlenbeck Type Process

Pages 33-44 | Received 01 Feb 2003, Accepted 01 Jun 2003, Published online: 19 Aug 2006

References

  • Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 2003 . Theory of Long-Range Dependence Boston : Birkhauser .
  • Henry , M. and Zafforoni , P. 2003 . “ The long-range dependence pardigm for macroeconomics and finance ” . In Theory of Long-Range Dependence Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 417 – 438 . Boston : Birkhauser .
  • Hurst , H.E. 1951 . Long term storage capacity of reservoirs (with discussion) . Trans. Am. Soc. Civ. Eng. , 116 : 770 – 808 .
  • Ikeda , N. and Watanabe , S. 1981 . Stochastic Differential Equations and Diffusion Processes Amsterdam : North-Holland .
  • Karatazas , I. and Shreve , S. 1988 . Brownian Motion and Stochastic Calculus Berlin : Springer .
  • Kleptsyna , M.L. and Le Breton , A. 2002 . Statistical analysis of the fractional Ornstein–Uhlenbeck type process . Statist. Inf. Stochast. Proces. , 5 : 229 – 248 . [CROSSREF]
  • Kleptsyna , M. L. , Le Breton , A. and Roubaud , M.-C. 2000 . Parameter estimation and optimal filtering for fractional type stochastic systems . Statist. Inf. Stochast. Proces. , 3 : 173 – 182 . [CROSSREF]
  • Le Breton , A. 1998 . Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion . Stat. Probab. Lett. , 38 : 263 – 274 . [CROSSREF]
  • Montanari , A. 2003 . “ Long-range dependence in hydrology ” . In Theory of Long-Range Dependence Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 461 – 472 . Boston : Birkhauser .
  • Norros , I. , Valkeila , E. and Virtamo , J. 1999 . An elementary approach to a Girsanov type formula and other analytical results on fractional Brownian motion . Bernoulli , 5 : 571 – 587 .
  • Norros , I. 2003 . “ Large deviations of queues with long-range dependent input ” . In Theory of Long-Range Dependence Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 409 – 415 . Boston : Birkhauser .
  • Novikov , A. A. 1972 . Sequential estimation of the parameters of diffusion proocesses . Mathematical Notes , 12 : 812 – 818 .
  • Prakasa Rao , B. L.S. 1987 . Asymptotic Theory of Statistical Inference New York : Wiley .
  • Prakasa Rao , B. L.S. 1999a . Statistical Inference for Diffusion Type Processes New York : Arnold, London and Oxford University Press .
  • Prakasa Rao , B. L.S. 1999b . Semimartingales and Their Statistical Inference London : CRC Press: Boca Raton and Chapman and Hall .
  • Prakasa Rao , B. L. S. 2003 . Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion . Random Oper. Stoch. Equ. , 11 : 229 – 242 . [CROSSREF]
  • Prakasa Rao , B.L.S. Berry–Esseen bound for MLE for linear stochastic differential equations driven by fractional Brownian motion, Indian Statistical Institute: New Delhi, Preprint, 2003a
  • Revuz , D. and Yor , M. 1991 . Continuous Martingales and Brownian Motion Berlin : Springer .
  • Taqqu , M. 2003 . “ Fractional Brownian motion and long-range dependence ” . In Theory of Long-Range Dependence Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 5 – 38 . Boston : Birkhauser .
  • Willinger , W. , Paxson , V. , Riedi , R.H. and Taqqu , M. 2003 . “ Long-range dependence and data network traffic ” . In Theory of Long-Range Dependence Edited by: Doukhan , P. , Oppenheim , G. and Taqqu , M.S. 373 – 407 . Boston : Birkhauser .
  • Recommended by N. Mukhopadhyay

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