B. Mandelbrot. Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics, 131:5--42, 1989. Home/Search Document Not in Database Summary Related Articles Check |
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Multifractal Processes - Riedi (1999) (7 citations) (Correct)
....subordination. 1 Introduction and Summary Fractal processes have been instrumental in a variety of fields ranging from the theory of fully developed turbulence [73, 64, 36, 12, 7] to stock market modelling [28, 68, 69, 80] image processing [61, 21, 104] medical data [2, 98, 11] and geophysics [36, 65, 47, 92]. In networking, models using fractional Brownian motion (fBm) have helped advance the field through their ability to assess the impact of fractal features such as statistical selfsimilarity and long range dependence (LRD) to performance [60, 81, 90, 89, 96, 34, 88] Roughly speaking, a fractal ....
B. Mandelbrot. Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics, 131:5--42, 1989.
Multifractal properties of Hao's geometric representations of DNA.. - Tino (Correct)
.... set of sequences speci ed by the underlying automaton) For a xed block length n, if we identi ed the n blocks with symbols in a larger alphabet A and assigned to symbols from A frequencies of the corresponding n blocks, Theorems 1 and 2 would be related to the results of Mandelbrot [26] and Guti errez and Rodriguez [27] concerning the f( multi15 fractal spectra (see next section) of single scaled multinomial measures 5 Geometric block representations of symbolic dynamical systems While in the previous section we analyzed geometric and measure scaling properties of various ....
B.B. Mandelbrot, Pure and Applied Geophysics 131 (1989) 5-42.
Multifractal Analysis of Choquet Capacities: Preliminary Results - Vehel, VOJAK (1995) (4 citations) (Correct)
....une suite de capacit es de Choquet dont le spectre de Holder est prescrit. Mots cl e : capacit es de Choquet, dimension de Hausdorff, spectres multifractals. 2 Jacques L EVY V EHEL, Robert VOJAK 1. Introduction Multifractal analysis was first introduced for the study of turbulence in [1, 2, 3, 4, 5, 6, 7]. It was then much developed in a mathematical framework for instance in [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] where general results were obtained for deterministic or random measures. Other authors extended this analysis to point functions ( 19, 20] obtaining quite complete descriptions. ....
.... g L(ff) fx 2 D = ff L (x) ff L g M(ff ) fx 2 D = ff (x) ff g where ff L (x) represents the Holder exponent of at x with respect to L. It is easy to see that E( M Gamma d b c Gamma a = L( d Gamma b) Using the Kinney Pitcher Billingsley theorem ( 25] 14.1 p. 141, [3]) we get 8 : ff = Gamma 0 log m 0 Gamma 1 log m 1 Gamma 0 log p 0 Gamma 1 log p 1 f h (ff ) dim M(ff ) Gamma 0 log 0 Gamma 1 log 1 Gamma 0 log p 0 Gamma 1 log p 1 Here, the f h spectrum has the familiar bell shape observed usually for ....
B.B. Mandelbrot. Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics, 131:5--42, 1989.
Multifractal Analysis of Choquet Capacities: Preliminary Results - Vehel, Vojak (1997) (4 citations) (Correct)
....and some preliminary results are presented concerning the usual spectra. In particular, we show how to construct a sequence of capacities whose Holder spectrum is, under mild conditions, prescribed. 1. Introduction Multifractal analysis was first introduced for the study of turbulence in [1, 2, 3, 4, 5, 6, 7] was then much developed in a mathematical framework for instance in [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18] where general results were obtained for deterministic or random measures. Other authors extended this analysis to point functions ( 19, 20] obtaining quite complete descriptions. In ....
....: fx 2 D = ff L (x) ff L g M(ff ) fx 2 D = ff (x) ff g where ff L (x) represents the Holder exponent of at x with respect to L. It is easy to see that E( M Gamma d b c Gamma a = L( d Gamma b) 17 Using the Kinney Pitcher Billingsley theorem ( 24] 14.1 p. 141, [3]) we get 8 : ff = Gamma 0 log m 0 Gamma 1 log m 1 Gamma 0 log p 0 Gamma 1 log p 1 f h (ff ) dim M(ff ) Gamma 0 log 0 Gamma 1 log 1 Gamma 0 log p 0 Gamma 1 log p 1 Here, the f h spectrum has the familiar bell shape observed ....
B.B. Mandelbrot. Multifractal measures, especially for the geophysicist. Pure and Applied Geophysics, 131:5--42, 1989.
Multifractality in Asset Returns: Theory and Evidence - Calvet, Fisher (2001) Self-citation (Mandelbrot) (Correct)
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Mandelbrot, B. B. (1989a), Multifractal Measures, Especially for the Geophysicist, Pure and Applied Geophysics 131, 5-42.
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