[1] Adler, R. (1981). Geometry of random fields. Wiley, New York. | MR | Zbl

[2] Arnold, V. et Avez, A. (1967). Problèmes ergodiques de la mécanique classique.. Gauthier-Villars, Paris. | MR | Zbl

[3] Babloyantz, A., Salazar, J.M. et Nicolis, C. (1985). Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys. Letters 111 152-156. | DOI

[4] Bailey, B., Ellner, S. et Nychka, D. (1997). Chaos with confidence : asymptotics and applications of local Lyapunov expnonents. In Fields Institute Communications 11 115-133 | MR | Zbl

[5] Bartlett, M.S. (1990). Chance or chaos ? J. R. Statist. Soc. A 153 321-347. | DOI

[6] Benedicks, M. and Carleson, L. (1991). The dynamics of the Hénon map. Ann. Math. 133 73-169. | MR | Zbl | DOI

[7] Bergé, P., Pomeau, Y., et Vidal, C. (1984). L'ordre dans le chaos. Herman, Paris.

[8] Bosq, D. (1995). Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data. J. Stat. Probab. Lett. 22 339-347. | MR | Zbl | DOI

[9] Bosq, D. et Guégan, D. (1995). Non parametric estimation of the chaotic function and the invariant measure of a dynamical system. J. Stat. Probab. Lett. 25 201-212. | MR | Zbl | DOI

[10] Casdagli, M. (1992). Chaos and deterministic versus stochastic non-linear modelling. J. R. Statist. Soc. B 54 303-328. | MR

[11] Cheng, B. et Tong, H. (1992). On consistent nonparametric order determination and chaos. J. R. Statist. Soc. B 54 427-449. | MR | Zbl

[12] Cutler, C.D. (1991). Some results on the behavior and estimation of the fractal dimensions of distributions on attractors. J. Statist. Phys. 62 651-708. | MR | Zbl | DOI

[13] Cutler, C.D. (1994). A theory of correlation dimension for stationary time series. Philos. Trans. R. Soc. Lond. A 348 343-355. | MR | Zbl | DOI

[14] Dahan Dalmenico, A., Chabert, J.L. et Chemla, K. (1992). Chaos et déterminisme. Seuil : Points sciences.

[15] Denker, M. et Keller, G. (1986). Rigorous statistical procedure for data from dynamical systems. J. Statist. Phys. 49 67-93. | MR | Zbl | DOI

[16] Ding, M., Gregobi, C., Ott, E., Sauer, T., and Yorke, J. (1993). Estimating correlation dimension from a chaotic time series : when does plateau onset occur ? Physica D 69 404-424. | MR | Zbl

[17] Eckmann, J.-P. and Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57 617-656. | MR | Zbl | DOI

[18] Falconer, K. (1990). Fractal geometry. Chichester : Wiley. | MR

[19] Feigenbaum, M.J. (1980). The transition to aperiodic behavior in turbulent systems. Comm. Math. Phys. 77 65-86. | MR | Zbl | DOI

[20] Feigenbaum, M.J., Kadanoff, L.P. and Shenker, S. J. (1982). Quasiperiodicity in dissipative systems: a renormalizion group analysis. Physica D 5 370-386. | MR

[21] Fraedrich, K. and Risheng, W. (1993). Estimating the correlation dimension of an attractor from noisy and small datasets based on re-embedding. Physica D 65 373-398 | MR | Zbl

[22] Gleick, J. (1991). La théoris du chaos. Flammarion : Champs.

[23] Grassberger, P. and Proccacia, I. (1983). Measuring the strangeness of strange attractors. Physica D 9 189-208. | MR | Zbl

[24] Guckeinheimer, J. and Holmes, P. (1986). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. | MR | Zbl

[25] Hènon, M. (1976). A two dimensional mapping with a strange attractor. Comm. Math. Phys. 50 69-77. | MR | Zbl | DOI

[26] Isham, V. (1993). Statistical aspects of chaos: a review. Networks and Chaos - Statistical and probabilistic aspects - Chapman and Hall, London, 124-200. | MR | Zbl

[27] Jensen, J.L.. (1993). Chaotic dynamical systems with a view towards statistics : a review. Networks and Chaos- Statistical and probabilistic aspects Chapman and Hall, London, 201-250. | MR | Zbl

[28] Kuhn, T.S. (1983). La structure des révolutions scientifiques. Flammarion : Champs.

[29] Lu, Z.Q. et Smith, R.L. (1997). Estimating local Lyapunov exponents. In Fields Institute Communications 11 135-151 | MR | Zbl

[30] Mccaffrey, D., Ellner, S., Gallant, A.R. et Nychka, D. (1992). Estimating the Lyapunov exponent of a chaotic system with non-parametric regression. J. Am. Statist. Ass. 86 682-695 | MR | Zbl | DOI

[31] Mandelbrot, B.B. (1995). Les objects fractals. Flammarion : Champs.

[32] Malraison, B., Atten, P., Bergé, P. et Dubois, M. (1984). Dimension of strange attractors: an experimental determination for the chaotic regime of two convective systems. J. Phys. Lett. 44 L-897. | DOI

[33] Marteau, P.F. and Abarbanel, H.D.I. (1991). Noise reduction in chaotic time series using scaled probabilistic methods. J. Nonlinear Sci. 1 313-343. | MR | Zbl | DOI

[34] Mayer-Kress, G. (1986). Dimensions and entropies in chaotic systems. New-York : Springer-Verlag. | MR | Zbl | DOI

[35] Nychka, D., Ellner, S., Gallant, A.R. and Mccaffrey, D. (1992). Finding chaos in noisy systems. J. R. Stat. Soc. B 54 399-426. | MR

[36] Ogata, Y. and Katsura, K. (1991). Maximum likelihood estimates of the fractal dimension for random spatial patterns. Biometrika 78 463-474. | MR | Zbl | DOI

[37] Ornstein, D.S. and Weiss, B. (1991). Statistical properties of chaotic systems. Bull. Am. Math. Soc. 24 11-116. | MR | Zbl | DOI

[38] Osborne, A.R. and Provenzale, A. (1989). Finite correlation dimension for stochastic systems with power-law spectra. Physica D 35 357-381. | MR | Zbl

[39] Pesin, Y.B. (1993). On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions. J. Statist. Phys. 71 529-547. | MR | Zbl | DOI

[40] Prigogine, I et Stengers, I. (1986). La nouvelle alliance. Gallimard : Folio essais..

[41] Provenzale, A. and Osborne, A.R. (1991). Deterministic chaos versus random noise : finite correlation dimension for colored noises with power-law power spectra. 260-275. | MR

[42] Rényi, A. (1970). Probability theory.. | MR | Zbl

[43] Ruelle, D. et Takens, (1971).. Comm. Math. Phys. 82 137-151. | MR | Zbl | DOI

[44] Ruelle, D. (1981). Small random perturbations of dynamical systems and the definition of attractors. Comm. Math. Phys. 82 137-151. | MR | Zbl | DOI

[45] Ruelle, D. (1989a). Chaotic evolution and strange attractors. Cambridge : Cambridge University Press. | MR | Zbl

[46] Ruelle, D. (1989b). Elements of differentiable dynamics and bifurcation theory. New-York : Academic Press. | MR | Zbl

[47] Ruelle, D. (1990). Deterministic chaos : the science and the fiction. Proc. R. Soc. Lond. B 427 241-248. | Zbl | MR

[48] Ruelle, D. (1991). Hasard et chaos Odile Jacob : Points.

[49] Scheinkman, J. (1994). Nonlinear dynamics in economics and finance. Philos. Trans. R. Soc. Lond. A 346 235-250. | MR | Zbl | DOI

[50] Serinko, R.J. (1994). A consistent approach to least squares estimation of correlation dimension in weak Bernoulli dynamical systems. Annals Appl. Probab. 4 1234-1254. | MR | Zbl | DOI

[51] Smith, R.L. (1992). Optimal estimation of fractal dimension. In Nonlinear modeling and forecasting, Proc. Vol. XII, Eds. M. Casdagli and S. Eubank, Addison-Wesley.

[52] Smith, R.L. (1992). Estimating dimension in noisy chaotic time series. J. R. Stat. Soc. B 54 329-351. | MR | Zbl

[53] Theiler, J. (1988). Lacunarity in a best estimator of fractal dimension. Physics Letters A 133 195-200. | MR | DOI

[54] Theiler, J. (1990). Statistical precision of dimension estimators. Physical Review A 41 3038-3051. | DOI

[55] Theiler, J. (1991). Some comments on the correlation dimension of $1/f^{\alpha }$ noise. Physics Letters A 155 480-493. | MR | DOI

[56] Tong, H. (1990). Nonlinear Times Series. Oxford, Oxford Univ. Press. | MR

[57] Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A. (1985). Determining Lyapunov exponents from a time series. Physica D 16 285-315. | MR | Zbl

[58] Wolff, R.C.L. (1992). Local Lyapunov exponents : looking closely at chaos. J. R. Stat. Soc. B 54 353-371. | MR

[59] Young, L.S. (1982). Dimension, entropy and Lyapunov exponents. Ergod. Theory Dynam. Syst. 2 109-124. | MR | Zbl | DOI

[1] Adler, R. (1981). Geometry of random fields. Wiley, New York. | MR | Zbl

[2] Berman, S. (1973). Local non-determinism and local times of Gaussian processes. Indiana Math. J. 23 69-94. | MR | Zbl | DOI

[3] Cutler, C. (1994). A theory of correlation dimension for stationary time series. Philos. Trans. R. Soc. Lond. A 348 343-355. | MR | Zbl | DOI

[4] Cuzick, J. (1978). Some local properties of Gaussian vector fields. Ann. Probab. 6 984-994. | MR | Zbl | DOI

[5] Cuzick, J. (1982). Multiple points of a Gaussian vector fields. Z. Warsch. Verw. Gebiete 61 431-436. | MR | Zbl | DOI

[6] Ding, M., Gregobi, C., Ott, E., Sauer, T., and Yorke, J. (1993). Estimating correlation dimension from a chaotic time series : when does plateau onset occur ? Physica D 69 404-424. | MR | Zbl

[7] Dynkin, E. (1988). Self-intersection gauge for random walks and for Brownian motion. Ann. Probab. 16 1-57. | MR | Zbl

[8] Eckmann, J.-P. and Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57 617-656. | MR | Zbl | DOI

[9] Feller, W. (1971). An introduction to probability theory and its applications. Vol. 2, Wiley. | MR

[10] Frostman, O. (1935). Potemtiel d'équilibre et capacité des ensembles, avec quelques applications à la théorie des fonctions. Medd. Lunds. Univ. Mat. Semin. 3. | JFM

[11] Geman, D. and Horowitz, J. (1980). Occupation densities. Ann. Probab. 8 1-67. | MR | Zbl | DOI

[12] Grassberger, P. and Proccacia, I. (1983). Measuring the strangeness of strange attractors. Physica D 9 189-208. | MR | Zbl

[13] Imkeller, P., Perez-Abreu, V. and Vives, J. (1995). Chaos expansions of double intersection local time of Brownian motion in ${ℝ}^d$ and renormalization. Stock. Pro. Appl. 56 1-34. | MR | Zbl | DOI

[14] Kametani, S. (1944). On Hausdorff's measures and generalized capacities with some of their applications to the theory of functions. Japanese J. Math. 19 217-257. | MR | Zbl | DOI

[15] Kono, N. (1978). Double points of a Gaussian path. Z. Warsch. Verw. Gebiete 45 175-180. | MR | Zbl | DOI

[16] Le Gall, J.F. (1985). Sur le temps local d'intersection du mouvement brownien plan et la méthode de renormalisation de Varadhan. Séminaire de Probabilités XIX. Lecture Notes in Math. 1123 314-331. | MR | Zbl | Numdam

[17] Pitt, L. (1978). Local times for Gaussian vector fields. Indiana Univ. Math. J. 27 309-330. | MR | Zbl | DOI

[18] Rosen, J. (1983). A local time approach to the self-intersections of Brownian paths in space. Comm. Math. Phys. 88 327-338. | MR | Zbl | DOI

[19] Rosen, J. (1984). Self-intersections of random fields. Ann. Probab. 12 108-119. | MR | Zbl | DOI

[20] Rosen, J. (1987). The intersection local time of fractional Brownian motion in the plane. J. Mult. Anal. 23 37-46. | MR | Zbl | DOI

[21] Rosen, J. (1988). Continuity and singularity of the intersection local time of stable processes in ${ℝ}^2$. Ann. Probab. 16 75-79. | MR | Zbl | DOI

[22] Smith, R.L. (1992). Estimating dimension in noisy chaotic time series. J. R. Stat. Soc. B 54 329-351. | MR | Zbl

[1] Abry, P. and Sellan, F. (1996). The wavelet-based synthesis for the fractional Brownian motion proposed by F. Sellan and Y. Meyer : remarks and fast implementation. Applied, and Computational Harmonic Analysis 3, 377-383. | MR | Zbl | DOI

[2] Azencott, R. and Dacunha-Castelle, D. (1984). Séries d'observations irrégulières. Masson, Paris. | MR | Zbl

[3] Beran, J (1994). Statistics for long memory processes. Monographs on Statist, and Appl. Probab. 61. Chapman & Hall, 315 p. | MR | Zbl

[4] Breuer, P. and Major, P. (1983). Central limit theorem for non-linear functionals of Gaussian fields. J. Multivariate Anal. 13, 425-441. | MR | Zbl | DOI

[5] Fox, R. and Taqqu, M.S. (1986). Large-sample properties of parameter estimates for strongly dependent Gaussian time series. Ann. Statist. 14, 517-532. | MR | Zbl

[6] Fox, R. and Taqqu, M.S. (1987). Central limits theorems for quadratic forms in random variables having long-range dependence. Probab. Theory Related Fields 74, 213-240. | MR | Zbl | DOI

[7] Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. J. Time Ser. Anal. 4, 221-238. | MR | Zbl | DOI

[8] Giraitis, L. and Surgailis, D. (1990). A central limit theorem for quadratic forms in strongly dependent linear variables and its applications to the asymptotic normality of Whittle estimate. Probab. Theory Related Fields 86, 87-104. | MR | Zbl | DOI

[9] Istas, J. and Lang, G. (1997). Quadratic variations and estimation of the local Holder index of a Gaussian process. Ann. Inst. Poincaré 33, 407-436. | MR | Zbl | Numdam | DOI

[10] Mandelbrot, B.B. (1983). The fractal geometry of nature. Freeman, San Francisco. | MR | Zbl

[11] Mandelbrot, B.B. and Van Ness, J.W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review 10, 422-437. | MR | Zbl | DOI

[12] Poggi, J.M. and Viano, M.C. (1996). An estimate of the fractal index using multiscale aggregates. To appear in J. Time Ser. Anal. | MR | Zbl

[13] Robinson, P.M. (1995). Log-periodogram regression of time series with long-range dependence. Ann. Statist. 23, 1048-1072. | MR | Zbl | DOI

[14] Samorodnitsky, G. and Taqqu, M.S. (1994). Stable non-Gaussian random processes. Stochastic modeling. Chapman & Hall, 636 p. | MR | Zbl

[15] Taqqu, M.S. (1975). Weak Convergence to Fractional Brownian Motion and to Rosenblatt Process. Zeit. Wahr. verw. Geb. 31, 287-302. | MR | Zbl | DOI

[16] Taqqu, M.S., Teverovsky, V. and Willinger, W. (1995). Estimators for long-range dependence: an empirical study. Fractals 3, 785-798. | Zbl | DOI

[17] Yajima, Y. (1989). Asymptotic properties of the LSE in a regression model with long-range stationary errors. Ann. Statist. 19, 158-177. | MR | Zbl

[1] Abry, P. and Sellan, F. (1996). The wavelet-based synthesis for the fractional Brownian motion proposed by F. Sellan and Y. Meyer : remarks and fast implementation. Applied and Computational Harmonic Analysis 3, 377-383. | MR | Zbl | DOI

[2] Abry, P., Goncalves, P. and Flandrin, P. (1995). Wavelets, spectrum analysis and $1/f$ processes. Wavelets and Statistics, Lectures Note in Statistics, 103, 15-29. | Zbl

[3] Abry, P. and Veitch D. (1997). Wavelet analysis of long range dependent traffic. To appear in IEEE Trans, on Inform. Theory. | MR | Zbl

[4] Abry, P., Veitch D. and Flandrin, P. (1997). Long-range dependence : revisiting aggregation with wavelets. To appear in J. Time Ser. Anal. | MR | Zbl

[5] Bardet, J.M. (1997). Testing self-similarity of Gaussian processes with stationary increments. Preprint Orsay.

[6] Beran, J (1994). Statistics for long memory processes. Monographs on Stat. and Appli. Prob. 61. Chapman & Hall, 315 p. | MR | Zbl

[7] Daubechies, I. (1992). Ten lectures on wavelets. CBMS, SIAM 61, Philadelphia. | MR | Zbl

[8] Flandrin, P. (1989). On the spectrum of fractional Brownian motions. IEEE Trans. on Info. Theory 35 197-199. | MR | DOI

[9] Flandrin, P. (1992). Wavelet analysis and synthesis of fractional Brownian motion. IEEE Trans. on Inform. Theory 38 910-917. | MR | Zbl | DOI

[10] Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. J. Time Ser. Anal. 4, 221-238. | MR | Zbl | DOI

[11] Giraitis, L. and Surgailis, D. (1990). A central limit theorem for quadratic forms in strongly dependent linear variables and its applications to the asymptotic normality of Whittle estimate. Probab. Theory Related Fields 86, 87-104. | MR | Zbl | DOI

[12] Goncalvès, P. and Abry, P. (1997). Multiple-window wavelet transform and local scaling exponent estimation. Preprint INRIA.

[13] Istas, J. and Lang, G. (1997). Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. Poincaré 33, 407-436. | MR | Zbl | Numdam | DOI

[14] Mandelbrot, B.B. (1983). The fractal geometry of nature. Freeman, San Francisco. | MR | Zbl | DOI

[15] Poggi, J.M. and Viano, M.C. (1996). An estimate of the fractal index using multiscale aggregates. To appear in J. Time Ser. Anal. | MR | Zbl

[16] Robinson, P.M. (1995). Log-periodogram regression of time series with long-range dependence. Ann. Statist. 23, 1048-1072. | MR | Zbl | DOI

[17] Samorodnitsky, G. and Taqqu, M.S. (1994). Stable non-Gaussian random processes. Stochastic modeling. Chapman & Hall, 636 p. | MR | Zbl

[18] Taqqu, M.S. (1975). Weak Convergence to Fractional Brownian Motion and to Rosenblatt Process. Z. Wahrscheinlichkeitstheorie verw. Geb. 31, 287-302. | MR | Zbl | DOI

[19] Taqqu, M.S., Teverovsky, V. and Willinger, W. (1995). Estimators for long-range dependence : an empirical study. Fractals 3, 785-798. | Zbl | DOI

[20] Yajima, Y. (1989). Asymptotic properties of the LSE in a regression model with long-range stationary errors. Ann. Statist. 19, 158-177. | MR | Zbl