A fractional linear system view of the fractional brownian motion

Nonlinear Dynamics

Volumn 38, Issue 1-4, 2004, Pages 295-303

  Ortigueira, Manuel Duarte ^a   Batista, Arnaldo Guimarães ^a  

^a UNINOVA   (Portugal)

Author keywords

Backward difference; Bilinear transformation; Fractional Brownian motion; Fractional differintegrator; Hurst parameter

Indexed keywords

COMPUTER SIMULATION; FUNCTIONS; LINEAR SYSTEMS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; TIME DOMAIN ANALYSIS;

BACKWARD DIFFERENCE; BILINEAR TRANSFORMATIONS; FRACTIONAL BROWNIAN MOTION; FRACTIONAL DIFFERINTEGRATORS; HURST PARAMETERS;

BROWNIAN MOVEMENT;

EID: 15544378664     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3762-8     Document Type: Conference Paper

References (13)

1. Mandelbrot, B. B. The Fractal Geometry of Nature, W. H. Freeman, New York, 1983.
2. Mandelbrot, B. B. and Van Ness, J. W. 'The fractional Brownian motions, fractional noises and applications', SIAM Review 10(6), 1968, 422-437.
3. Keshner, M. S. '1/f Noise', Proceedings of IEEE 70, March 1982, 212-218.
4. Reed, I. S., Lee, P. C., and Truong, T. K. 'Spectral representation of fractional Brownian motion in ndimensions and its properties ', IEEE Transactions on Information Theory 41(8), 1995, 1439-1451.
5. Ortigueira, M. D. 'Introduction to fractional signal processing. Part 1: Continuous-time systems', IEE Proceedings on Vision, Image and Signal Processing 1, February 2000, 62-70.
6. Li, M. and Chi, C-H. 'A correlation-based computational model for synthesizing long-range dependent data', Journal of the Franklin Institute 340, 2003, 503-514.
7. Henrici, P. Applied and Computational Complex Analysis, Vol. 2, Wiley, New York, pp. 389-391, 1991.
8. Samko, S. G., Kilbas, A. A. and Marichev, O. I., Fractional Integrals and Derivatives - Theory and Applications, Gordon and Breach, Amsterdam, 1993.
9. Hosking, J. 'Fractional differencing', Biometrika 68, 1981, 165-176.
10. Ortigueira, M. D. 'Introduction to fractional signal processing. Part 2: Discrete-time systems', IEE Proceedings on Vision, Image and Signal Processing 1, February 2000, 71-78.
11. Taqqu, M. S., Teverovsky, V., and Willinger, W. 'Estimators for long-range dependence: an empirical study', Fractals 3(4), 1995, 785-788.
12. Karagiannis, T., Faloutsos, M., and Riedi, R. H. 'Long-range dependence: Now you see it, now, you don't!', in Proceedings Global Internet, Taiwan, November 2002.
13. Chang, Y.-C. and Chang, S. 'A fast estimation Algorithm on the Hurstparameter of discrete-time fractional Brownian motion', IEEE Transactions on Signal Processing 50(3), March 2002, 554-559.