Journal of the Korean Statistical Society

  • 제34권4호
  • /
  • Pages.281-295
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  • 2005
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  • 1226-3192(pISSN)
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  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

BERRY-ESSEEN BOUND FOR MLE FOR LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

  • RAO B.L.S. PRAKASA (Department of Mathematics and Statistics, University of Hyderabad)
  • 발행 : 2005.12.01
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초록

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

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참고문헌

  1. ALOS, E., MAZET, O., AND NUALART, D. (2001). 'Stochastic calculus with respect to gaussian processes', Annals of Probability, 29, 766-801 https://doi.org/10.1214/aop/1008956692
  2. BOSE, A. (1986). 'Berry-Esseen bound for the maximum likelihood estimator in the Ornstein-Uhlenbeck process', Sankhya Ser.A, 48, 181-187
  3. FELLER, W. (1968). An Introduction to Probability Theory and its Applications, Wiley, New York
  4. HALL, P. AND HEYDE, C.C. (1980). Martingale Limit Theory and its Applications, Academic Press, New York
  5. IKEDA, N. AND WATANABE, S. (1981). Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam
  6. KLEPTSYNA, M.L. AND LE BRETON, A. (2002). 'Statistical analysis of the fractional Ornstein-Uhlenbeck type process', Statistical Inference for Stochastic Processes, 5, 229-248 https://doi.org/10.1023/A:1021220818545
  7. KLEPTSYNA, M.L. AND LE BRETON, A. AND ROUBAUD, M.-C. (2000). 'Parameter estimation and optimal filtering for fractional type stochastic systems', Statistical Inference for Stochastic Processes. 3. 173-182 https://doi.org/10.1023/A:1009923431187
  8. LE BRETON, A. (1998). 'Filtering and parameter estimation in a simple linear model driven by a fractional Brownian motion', Statistical Probability Letters, 38, 263-274 https://doi.org/10.1016/S0167-7152(98)00029-7
  9. MICHEL, R. AND PFANZAGL, J. (1971). 'The accuracy of the normal approximation for minimum contrast estimate', Z. Wahr. verw Gebeite, 18, 73-84 https://doi.org/10.1007/BF00538488
  10. 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 https://doi.org/10.2307/3318691
  11. PRAKASA RAO, B.L.S. (1987). Asymptotic Theory of Statistical Inference, Wiley, New York
  12. PRAKASA RAO, B.L.S. (1999). Statistical Inference for Diffusion Type Processes, Arnold, London and Oxford University Press, New York
  13. PRAKASA RAO, B.L.S. (2003). 'Parametric estimation for linear stochastic differential equations driven by fractional Brownian motion', Random Operators and Stochastic Equations, 11, 229-242 https://doi.org/10.1163/156939703771378581
  14. SAMKO, S.G., KILBAS, A.A., AND MARICHEV, O.I. (1993). Fractional Integrals and derivatives, Gordon and Breach Science, Yverdon
  15. WATSON, G.N. (1995). A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge