论文信息 - Identifying the multifractional function of a Gaussian process

Identifying the multifractional function of a Gaussian process

Gaussian processes that are multifractional are studied in this paper. By multifractional processes we mean that they behave locally like a fractional Brownian motion, but the fractional index is no more a constant: it is a function. We introduce estimators of this multifractional function based on discrete observations of one sample path of the process and we study their asymptotical behavior as the mesh decreases to zero.

[1] Andrew T. A. Wood,et al. On the performance of box-counting estimators of fractal dimension , 1993 .

[2] J. Lévy-Véhel. Introduction to the multifractal analysis of images , 1998 .

[3] J. L. Véhel,et al. MULTIFRACTAL SEGMENTATION OF IMAGES , 1994 .

[4] Stéphane Jaffard,et al. Identification of Elliptic Gaussian Random Processes , 1997 .

[5] B. Mandelbrot,et al. Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[6] R. Peltier,et al. Multifractional Brownian Motion : Definition and Preliminary Results , 1995 .

[7] Gabriel Lang,et al. Quadratic variations and estimation of the local Hölder index of a gaussian process , 1997 .

[8] Michael Ghil,et al. Turbulence and predictability in geophysical fluid dynamics and climate dynamics , 1985 .

[9] Andrew T. A. Wood,et al. ESTIMATION OF FRACTAL INDEX AND FRACTAL DIMENSION OF A GAUSSIAN PROCESS BY COUNTING THE NUMBER OF LEVEL CROSSINGS , 1994 .

[10] Stéphane Jaffard,et al. Identification of filtered white noises , 1998 .

[11] Jacques Lévy Véhel,et al. Change detection in sequences of images by multifractal analysis , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.