Fractal Dimension for Fractal Structures

Fractal Dimension for Fractal Structures

by Manuel Fernández-MartínezJuan Luis García Guirao Miguel Ángel Sánchez-Granero and others
Epub (Kobo), Epub (Adobe)
Publication Date: 07/07/2019

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This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts.


In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithmsfor properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes.


This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.

ISBN:
9783030166458
9783030166458
Category:
Calculus & mathematical analysis
Format:
Epub (Kobo), Epub (Adobe)
Publication Date:
07-07-2019
Language:
English
Publisher:
Springer International Publishing

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