References
- Arneodo, A., d’Aubenton Carafa, Y., Bacry, E., Grave, P.V., Muzy, J.F., Thermes, C. (1996). Wavelet based fractal analysis of DNA sequences. Phys. D Nonlin. Phenomena 96:291–320.
- Bardet, J.M., Philippe, A., Oppenheim, G., Taqqu, M.S., Stoev, S.A., Lang, G. (2003). Semi-parametric estimation of the long-range dependence parameter: A survey. Theor. Applic. Long-range Depend. 2003:557–577.
- Beran, J. (1994). Statistics for Long-memory Processes. New York: Chapman & Hall/CRC.
- Biskamp, D. (1994). Cascade models for magnetohydrodynamic turbulence. Phys. Rev. E 50:2702–2711.
- Breton, J.-C., Coeurjolly, J.-F. (2012). Confidence intervals for the hurst parameter of a fractional brownian motion based on concentration inequalities. Statist. Infer. Stoch. Proc. 15:1–26.
- Breton, J.C., Nourdin, I., Peccati, G. (2009). Exact confidence intervals for the hurst parameter of a fractional brownian motion. Electron. J. Statist. 3:416–425.
- Coeurjolly, J.-F. (2001). Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Statist. Infer. Stoch. Proc. 4:199–227.
- Coeurjolly, J.-F. (2008). Hurst exponent estimation of locally self-similar gaussian processes using sample quantiles. Ann. Statist. 36:1404–1434.
- Daubechies, I. (2006). Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41:909–996.
- Doukhan, P., Oppenheim, G., Taqqu, M.S. (2003). Theory and Applications of Long-range Dependence. Boston: Birkhauser.
- Horbury, T.S., Forman, M., Oughton, S. (2008). Anisotropic scaling of magnetohydrodynamic turbulence. Phys. Rev. Lett. 101:175005.
- Kolmogorov, A.N. (1941). The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30:9–13.
- Mandelbrot, B., Ness, J.V. (1968). Fractional brownian motions, fractional noises and applications. SIAM Rev. 10:422–437.
- Nelkin, M. (1975). Scaling theory of hydrodynamic turbulence. Phys. Rev. A 11:1737–1743.
- Nourdin, I., Réveillac, A. (2009). Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H= 1/4. Ann. Probab. 37:2200–2230.
- Peligrad, M., Sethuraman, S. (2008). On fractional brownian motion limits in one dimensional nearest-neighbor symmetric simple exclusion. Latin Amer. J. Probab. Mathemat. Statist. 4:245–255.
- Percival, D.B., Walden, A.T. (2000). Wavelet Methods for Time Series Analysis. Cambridge:Cambridge University Press.
- Pérez, D.G., Zunino, L., Garavaglia, M. (2004). Modeling turbulent wave-front phase as a fractional Brownian motion: a new approach. J. Opt. Soc. Amer. A 21: 1962–1969.
- Ribak, E. (1997). Atmospheric turbulence, speckle, and adaptive optics. Ann. New York Acad. Sci. 808:193–204.
- Schwartz, C., Baum, G., Ribak, E. (1994). Turbulence-degraded wave fronts as fractal surfaces. J. Opt. Soc. Amer. A 11:444–451.
- Swanson, J. (2010). Fluctuations of the empirical quantiles of independent brownian motions. Stoch. Process. Applic. 121:479–514.
- Veitch, D., Abry, P. (1999). A wavelet-based joint estimator of the parameters of long-range dependence. IEEE Trans. Inform. Theory. 45:878–897.