Multifractals: Theory and ApplicationsCRC Press, 26. lip 2001. - Broj stranica: 264 Although multifractals are rooted in probability, much of the related literature comes from the physics and mathematics arena. Multifractals: Theory and Applications pulls together ideas from both these areas using a language that makes them accessible and useful to statistical scientists. It provides a framework, in particular, for the evaluation |
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2 The Multifractal Formalism | 29 |
3The Multinomial Measure | 47 |
4 Lattice Based Multifractals | 61 |
5 Point Centred Multifractals | 77 |
6 Multiplicative Cascade Processes | 89 |
7 Interpoint Distances of Order q and Intrinsic Bias | 113 |
8 Estimation of Point Centred R180enyi Dimensions with q 2 | 127 |
9 Extrinsic Sources of Bias | 155 |
10 Applications of Dimension Estimation | 165 |
11 Earthquake Analyses | 195 |
APPENDIX A Properties and Dimensions of Sets | 217 |
APPENDIX B Large Deviations | 225 |
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½ ¾ ½¼¼ ½¾ ½µ ¼ ½ ¾ Ê ÂÒ µ Assume bias bootstrap boundary effect Cantor measure Cantor set Chapter Co(q Corollary correlation dimension correlation integral cumulant generating function deep events defined Definition denoted describe dimension estimates discussed ÐÑ dynamical systems epicentres estimates of ¾ Example exponent Extended Hypotheses 4.2.2 Falconer finite fractal set Further given by Equation Hausdorff dimension hence Hill estimates hypocentres interpoint distances interval Kanto Earthquake lacunary cycles large deviations lattice Legendre transform logistic map Lorenz Attractor Mandelbrot Moran cascade process multifractal measure multifractal spectrum multinomial measures Ñ µ ѵ Ò ½ Ô¼ Õµ plotted in Figure point centred powerlaw behaviour probability distribution probability measure R´enyi dimensions random variables region rescaled cumulant sampling measure satisfies the Extended scaling self-similar sequence shallow events simulated slope spatial stochastic processes subintervals subset ܵ values Wellington width ݴѵ ݵ zero