{ "item_title" : "Multifractals", "item_author" : [" David Harte "], "item_description" : "Although multifractals are rooted in probability, most of the related literature comes from the physics arena, where the treatments lack the rigor, proper framework, and language to make them accessible and useful to statistical scientists. Multifractals: Theory and Applications pulls together ideas from the different areas to place the material into a probabilistic and statistical context and provides a framework for the statistical properties of the various estimates of fractal dimension.The first section provides the relevant background material and summarizes the results from large deviations, including the different definitions of dimension and the ideas of power law scaling and self similarity. The author then examines some of the various constructions for describing multifractal measures. Building on the theory of large deviations, he focuses on the constructions based on lattice coverings and on point centered spheres. The final section presents estimators defined for all Renyl dimensions and discusses their properties. It provides detailed case studies where dimensions are estimated and offers an interpretation of each.Estimating fractal dimensions holds particular value in studies of nonlinear dynamical systems, time series, and spatial point patterns. With its careful yet practical blend of multifractals, estimation methods, and case studies, Multifractals: Theory and Applications provides a unique opportunity to explore the estimation methods from a statistical perspective.", "item_img_path" : "https://covers1.booksamillion.com/covers/bam/1/58/488/154/1584881542_b.jpg", "price_data" : { "retail_price" : "225.00", "online_price" : "225.00", "our_price" : "225.00", "club_price" : "225.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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