Navigating Scaling: Modelling and Analysing
Patrice Abry, P. Goncalves, Patrick Flandrin, Darryl Veitch, Pierre Chainais, Bruno Lashermes, Nicolas Hohn, S. G. Roux, Pierre Borgnat, Murad S. Taqqu, Vladas Pipiras, Rudolf H. Riedi, Stéphane Jaffard · Defense Technical Information Center (DTIC) · 2005
I. INTUITIONS, MODELS, TOOLS: (1) Intuitions, Definition, Applications; (2) Stochastic Models: Self-Similarity vs Multifractal; (3) Multiresolution Tools, Aggregation, Increments; (4) Wavelets, Continuous, Discrete. II. SECOND ORDER ANALYSIS, SELF SIMILARITY AND LONG MEMORY: (1) Random Walks, Self-Similarity, Long Memory; (2) 2nd Order Wavelet Statistical Analysis; (3) Estimation, Estimation Performance; (4) Robustness Against Non-Stationarities. III. HIGHER ORDER ANALYSIS, MULTIFRACTAL PROCESSES: (1) Multiplicative Cascades, Multifractal Processes; (2) Higher Order Wavelet Statistical Analysis; (3) Finiteness of Moments; (4) Estimation, Estimation Performance; (5) Negative Orders; (6) Beyond Power Laws.