Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion

Statistics and Probability Letters

Volumn 38, Issue 3, 1998, Pages 263-274

  Breton, Alain Le ^a  

^a UNIV GRENOBLE ALPES   (France)

Author keywords

Best linear unbiased estimator; Fractional Brownian motion; Maximum likelihood estimator; Optimal filter

Indexed keywords

EID: 0032525495     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(98)00029-7     Document Type: Article

References (20)

1. Beran, J., 1992. Statistical models for data with long-range dependence Statis. Sci. 7, 404-427.
2. Beran, J., 1994. Statistics for Long-Memory Processes. Chapman & Hall, New York.
3. Comte, F., 1994. Simulation and estimation of long memory continuous time models J. Time Ser. Anal. 17 (1) 19-36.
4. Coelho, R., Decreusefond L., 1995. Video correlated traffic models for broadband communications networks. In Proceedings of the ITC Seminar on Teletraffic Management, vol.17, (1), pp. 19-36.
5. Dai, W., Heyde, C.C., 1996. Itô's formula with respect to fractional Brownian motion and its application. J. Appl. Math. Stochastic Anal. 9 (4), 439-448.
6. Decreusefond, L., Üstünel, A.S., 1996. Stochastic analysis of the fractional Brownian motion. Potential Analysis, to appear.
7. Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil Eng. 116, 400-410.
8. Hurst, H.E., 1956. Methods of using long-term storage in reservoirs Proc. Inst. Civil Engineers, Part I, Chapter 5, pp. 519-590.
9. Gripenberg, G., Norros, I., 1996. On the prediction of fractional Brownian motion J. Appl. Probab. 33, 400-410.
10. Kleptsyna, M.L., Kloeden, P.E., Anh, V.V., 1996a. Linear filtering with fractional Brownian motion. Stochastic Analysis and its Applications, to appear.
11. Kleptsyna, M.L., Kloeden, P.E., Anh, V.V., 1996b. Nonlinear filtering with fractional Brownian motion. Preprint.
12. Kleptsyna, M.L., Kloeden, P.E., Anh, V.V., 1996c. Linear filtering with fractional Brownian motion in the signal and observation processes. Preprint.
13. Leland, W.E., Taqqu, M.S., Willinger, W., Wilson D.V., 1994. On the self-similar nature of Ethernet traffic IEEE/ACM Trans. Networking 2 (1), 1-15.
14. Liptser, R.S., Shiryaev, A.N., 1978 Statistics of Random Processes, Springer, New York.
15. Lundgren, T., Chiang, D. 1967. Solution of a class of singular integral equations. Quart J. Appl. Math. 24, 303-313.
16. Mandelbrot, B.B., Van Ness, J.W., 1968. Fractional Brownian motions fractional noises and applications. SIAM Rev. 2 (10), 422-437.
17. Norros, I., 1994. A storage model with self-similar input. Queueing Systems 16, 387-396.
18. Norros, I., 1995. On the use of the fractional Brownian motion in the theory of correctionless networks. IEEE J. Sel. Ar. Comm. 13 (6), 953-962.
19. Norros, I., Valkeila, E., Virtamo, J., 1996. An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernouilli, to appear.
20. Samorodnitsky, G., Taqqu, M.S., 1994. Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall, London.