Multifractals: Theory and Applications 1st Edition by David Harte (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Compared to the recently republished papers of Mandelbrot, i had hoped much more from this book. It merely summarizes the existing work on multifractals without providing much insight about why is multifractal theory interesting in practice. If you are interested in a very good mathematical treatment go to the homepage of Rudolf Riedi at Rice University and read his papers. For the original ideas about multifractals and a far more applied perspective go to Mandelbrot’s books and also “Critical phenomena in natural sciences” by Sornette, you’ll get a more balanced theory-practice mix than in the present book. The only merit of this book is to reference quite fairly the existing literature, but this should not be the sole aim of a book, so i think that with this one you’ll waste your time.

⭐my addressErnst-Moritz-Arndt-Uni.institut mathematik und informatikFriedrich – Ludwig -jahn str. 15a17487 Greifswald – Germany

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