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45. J. Levy Vehel and R. Riedi. Fractional Brownian Motion and data traf c modeling: The other end of the spectrum. J. Levy Vehel, E. Lutton, and C. Tricot, eds., Fractals in Engineering, pp., 185 203. Springer, London, 1997. 46. S. Mallat. A Wavelet Tour of Signal Processing. Academic Press, Boston, 1997. 47. Y. Meyer, F. Sellan, and M. S. Taqqu. Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motion. Preprint, 1998. 48. S. M. Kay. Fundamentals of Statistical Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, 1993. 49. E. Masry. The wavelet transform of stochastic processes with stationary increments and its application to fractional Brownian motion. IEEE Trans. Inf. Theory, 39(1):260 264, 1993. 50. B. B. Mandelbrot and J. W. Van Ness. Fractional Brownian motions, fractional noises and applications. SIAM Rev., 10:422 437, 1968. 51. B. B. Mandelbrot. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech., 62(2): 331 358, 1974. 52. J. F. Muzy, E. Bacry, and A. Arneodo. The multifractal formalism revisited with wavelets. Int. J. Bifurc. Chaos, 4(2):245 301, 1994. 53. I. Norros, P. Mannersalo, and J. L. Wang. Simulation of fractional Brownian motion with conditionalized random midpoint displacement. Preprint, Oct. 1998. 54. A. Papoulis. Probability, Random Variables, and Stochastic Processes, 2nd ed. McGrawHill, New York, 1984. 55. V. Paxson. Fast approximation of self-similar network traf c. Preprint, 1995. 56. R. Peltier and J. Levy-Vehel. Multifractional Brownian motion: de nition and preliminary results. Submitted to Stochastic Processes and Their Applications, 1997. 57. B. Pesquet-Popescu. Statistical properties of the wavelet decomposition of some nonGaussian self-similar processes. Invited paper, Signal Processing 75(3): pp. xx xx, 1999. 58. B. Pesquet-Popescu, and P. Abry. Wavelet based estimators for the self-similarity parameter of a-stable processes. In preparation, 1999. 59. R. H. Riedi. An improved multifractal formalism and self-similar measures. J. Math. Anal. Appl., 189:462 490, 1995. 60. R. Riedi, M. S. Crouse, V. J. Ribeiro, and R. G. Baraniuk. A multifractal wavelet model with application to network traf c. IEEE Trans. Inf. Theory, Special issue on Multiscale Statistical Signal Analysis and Its Applications, 45(3): 992 1018, April 1999. 61. R. Riedi and J. Levy Vehel. TCP traf c in multifractal: a numerical study. Submitted to IEEE Trans. Networking. 62. M. Roughan, D. Veitoch, and P. Abry. On-line estimation of LRD parameters. In Proc. Globecom '98, Sydney, pp. 3716 3721, 1998. 63. S. Roux, J. F. Muzy, and A. Arneodo. Detecting vorticity laments using wavelet analysis: about the statistical contribution of vorticity laments to intermittency in swirling turbulent ows. Eur. Phys. J. B8: 301 322, 1998. 64. F. Sellan. Synthese de mouvements browniens fractionnaires a l'aide de la transformation par ondelettes. C.R. Acad. Sci. Ser. I, 321:351 358, 1995. 65. V. Teverovsky and M. S. Taqqu. Testing for long-range dependence in the presence of shifting means or a slowly declining trend using a variance-type estimator. J. Time Series Anal., 18:279 304, 1997.
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66. V. Teverovsky, M. S. Taqqu, and W. Willinger. A critical look at Lo's modi ed R=S statistics. J. Statist. Planning Inference, 80: 211 227, 1999. 67. G. Samorodnitsky and M. S. Taqqu. Stable Non-Gaussian Processes: Stochastic Models with In nite Variance. Chapman and Hall, New York, 1994. 68. M. S. Taqqu, V. Teverovsky, and W. Willinger. Estimators for long-range dependence: an empirical study. Fractals, 3(4):785 798, 1995. Reprinted in C. J. G. Evertsz, H.-O. Peitgen, and R. F. Voss, eds., Fractal Geometry and Analysis. World Scienti c Publishing, Singapore, 1996. 69. M. S. Taqqu and V. Teverovsky. Semi-parametric graphical estimation techniques for longmemory data. In P. M. Robinson and M. Rosenblatt, eds., Athens Conference on Applied Probability and Time Series Analysis. Volume II: Time Series Analysis in Memory of E. J. Hannan, Lecture Notes in Statistics 115, pp. 420 432. Springer-Verlag, New York, 1996. 70. M. S. Taqqu, V. Teverovsky, and W. Willinger. Is network traf c self-similar or multifractal Fractals, 5:63 74, 1997. 71. M. S. Taqqu and V. Teverovsky. On estimating the intensity of long-range dependence in nite and in nite variance series. In R. Adler, R. Feldman, and M. S. Taqqu, eds., A Practical Guide to Heavy Tails: Statistical Techniques and Applications. Birkhauser, Boston, 1998. 72. M. S. Taqqu and V. Teverovsky. Robustness of Whittle-type estimates for time series with long-range dependence. Stoch. Models, 13:723 757, 1997. 73. A. H. Tew k and M. Kim. Correlation structure of the discrete wavelet coef cients of fractional Brownian motion. IEEE Trans. Inf. Theory, 38:904 909, 1992. 74. D. Veitch and P. Abry. Estimation conjointe en ondelettes des parametres du phenonene de dependance longue. In Proc. 16ieme Colloque GRETSI, Grenoble, France, pp. 1451 1454, 1997. 75. D. Veitch and P. Abry. A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Trans. Inf. Theory, Special Issue on Multiscale Statistical Signal Analysis and its Applications, 45(3): 878 897, April 1999. 76. D. Veitch, P. Abry, and J. Bolot. Wavelet tools for the analysis of scaling phenomena in traf c. Preprint, 1999. 77. D. Veitch and P. Abry. A statistical test for the constancy of scaling exponents. Preprint, 1998. 78. W. Willinger, M. S. Taqqu, R. Sherman, and D. V. Wilson. Self-similarity through highvariability: statistical analysis of Ethernet LAN traf c at the source leve. IEEE=ACM Trans. Networking, 5(1):71 86, 1997. Extended version of the paper with the same title that appeared in Comput. Commun. Rev., 25:100 113, 1995. 79. G. W. Wornell and A. V. Oppenheim. Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process., 40(3):611 623, 1992. 80. G. W. Wornell. Signal Processing with Fractals: A Wavelet-Based Approach. Prentice-Hall, Englewood Cliffs, NJ, 1995.
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Self-Similar Network Traf c and Performance Evaluation, Edited by Kihong Park and Walter Willinger Copyright # 2000 by John Wiley & Sons, Inc. Print ISBN 0-471-31974-0 Electronic ISBN 0-471-20644-X
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