Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S [Hardcover]

Benoit Mandelbrot is a world-renowned scientist whose pioneering research significantly advanced the field of fractal geometry. This is the third volume of his Selected Works, focusing on a detailed study of fraction Brownian motions. The fractal themes of self-affinity and globality are presented. Extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools discussed will be valuable to diverse scientific communities.Advances in Old But Open Topics.- Broad Continuing Issues.- Introductions from the 1960s.- Fractional Brownian Motions.- Fractional Brownian Surfaces.- Self-Affine Cartoons in Grids; Their Multiple Fractal Dimensions.- R/S Analysis and Its Uses.

From the reviews of the first edition:

Written in Mandelbrots unique, thought-provoking style, these papers and commentaries contain a wealth of ideas which will appeal to mathematicians, statisticians, scientists and economists alike. It is a book both for dipping into and for detailed study, making readily accessible seminal papers which contain ideas that are as relevant now as when first published. (K. Falconer, Proceedings of the Edinburgh Mathematical Society, Vol. 48, 2005)

This book contains the authors works in areas ranging from statistics, mathematics, physics, hydrology to economics and finance & as well as more than 200 pages of new material written especially for this volume. & To summarize, Volume H of Mandelbrots Selecta is a major contribution to the understanding of wild self-affine variability and randomness. I believe that & it will have a great impact on future research in mathematics, statistics, physics and other applied areas. (Yimin Xiao, Zentralblatt MATH, Vol. 1007, 2003)

This book is a complete and encyclopaedic synthesis of problems and themes in self-affinity, fractals, multilÃ<