Rate Optimality of Wavelet Series Approximations of Fractional Brownian Motion

Journal of Fourier Analysis and Applications

Volumn 9, Issue 5, 2003, Pages 451-471

  Ayache, Antoine ^a   Taqqu, Murad S ^b  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b NONE

Author keywords

Best approximation; Fractional Brownian motion; Self similarity

Indexed keywords

EID: 0742306489     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00041-003-0022-0     Document Type: Article

References (13)

1. Abry, P., Flandrin, P., Taqqu, M.S., and Veitch, D. (2000). Wavelets for the analysis, estimation and synthesis of scaling data, in Self-Similar Network Traffic and Performance Evaluation, Park, K. and Willinger, W., Eds., 39-88, New York, Wiley (Interscience Division).
2. Burrus, C.S., Gopinath, R.A., and Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms, Prentice Hall.
3. Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM Philadelphia, CBMS-NSF series, Vol. 61.
4. Doukhan, P., Oppenheim, G., and Taqqu, M.S., Eds., (2002). Long-range Dependence: Theory and Applications, Birkhäuser, Boston.
5. Kühn, T. and Linde, W. (2002). Optimal series representation of fractional Brownian sheets, Bernoulli, 8(5), 669-696.
6. Ledoux, M. and Talagrand, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes, Springer-Verlag, New York.
7. Leland, W.E., Taqqu, M.S., Willinger, W., and Wilson, D.V. (1994). On the self-similar nature of Ethernet traffic (Extended version), IEEE/ACM Transactions on Networking, 2, 1-15.
8. Lemarié, P.G. and Meyer, Y. (1986). Ondelettes et bases hilbertiennes, Revista Matematica Iberoamericana, 2, 1-18.
9. Lifshits, M.A. (1995). Gaussian Random Functions, Kluwer, Dordrecht.
10. Meyer, Y. (1992). Ondelettes et Algorithmes Concurrents, Hermann, Paris.
11. Meyer, Y., Sellan, F., and Taqqu, M.S. (1999). Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motion, J. Fourier Anal. and Appl., 5(5), 465-494.
12. Samorodnitsky, G. and Taqqu, M.S. (1994). Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance, Chapman and Hall, New York, London.
13. Taqqu, M.S., Willinger, W., and Sherman, R. (1997). Proof of a fundamental result in self-similar traffic modeling, Computer Communications Review, 27(2), 5-23.