Manuel Fernández-Martínez: Fractal Dimension for Fractal Structures, Gebunden
Fractal Dimension for Fractal Structures
- With Applications to Finance
(soweit verfügbar beim Lieferanten)
- Verlag:
- Springer International Publishing, 05/2019
- Einband:
- Gebunden, HC runder Rücken kaschiert
- Sprache:
- Englisch
- ISBN-13:
- 9783030166441
- Artikelnummer:
- 9002958
- Umfang:
- 224 Seiten
- Nummer der Auflage:
- 19001
- Ausgabe:
- 1st edition 2019
- Gewicht:
- 506 g
- Maße:
- 241 x 160 mm
- Stärke:
- 18 mm
- Erscheinungstermin:
- 8.5.2019
- Hinweis
-
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.
