Fractal Dimension for Fractal Structures : With Applications to Finance. 1st ed. 2019

種類:

電子ブック

責任表示:

by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Fernández-Martínez, Manuel.
• García Guirao, Juan Luis.
• Sánchez-Granero, Miguel Ángel.
• Trinidad Segovia, Juan Evangelista.
• SpringerLink (Online service)

シリーズ名:

SEMA SIMAI Springer Series ; 19

ISBN:

9783030166458 [3030166457]    

注記:

1 Mathematical background -- 2 Box dimension type models -- 3 A middle definition between Hausdorff and box dimensions -- 4 Hausdorff dimension type models for fractal structures.
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 algorithms for properly calculating the self-similari

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