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Books > Science & Mathematics > Physics > Classical mechanics > Fluid mechanics
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Multifractals - Theory and Applications (Paperback)
Loot Price: R1,953
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Multifractals - Theory and Applications (Paperback)
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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 of statistical properties of
estimates of the Renyi fractal dimensions. The first section
provides introductory material and different definitions of a
multifractal measure. The author then examines some of the various
constructions for describing multifractal measures. Building from
the theory of large deviations, he focuses on constructions based
on lattice coverings, covering by point-centered spheres, and
cascades processes. The final section presents estimators of Renyi
dimensions of integer order two and greater and discusses their
properties. It also explores various applications of dimension
estimation and provides a detailed case study of spatial point
patterns of earthquake locations. 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.
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