Manuel Fernández-Martínez: Fractal Dimension for Fractal Structures
Manuel Fernández-Martínez
, Juan Evangelista Trinidad Segovia
, Miguel Ángel Sánchez-Granero
, Juan Luis García Guirao
Fractal Dimension for Fractal Structures
Buch
- With Applications to Finance
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EUR 131,42**
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- Springer International Publishing AG, 05/2019
- Einband: Gebunden, HC runder Rücken kaschiert
- Sprache: Englisch
- ISBN-13: 9783030166441
- Bestellnummer: 9002958
- Umfang: 224 Seiten
- Nummer der Auflage: 19001
- Auflage: 1st ed. 2019
- Gewicht: 506 g
- Maße: 241 x 160 mm
- Stärke: 18 mm
- Erscheinungstermin: 8.5.2019
- Serie: SEMA SIMAI Springer Series - Band 19
Achtung: Artikel ist nicht in deutscher Sprache!
Klappentext
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.