| Dewey Class |
515.39 |
| 515.48 |
| Title |
Fractal Dimension for Fractal Structures ([EBook]) : With Applications to Finance / by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia. |
| Author |
Fernández-Martínez, Manuel |
| Added Personal Name |
García Guirao, Juan Luis |
| Sánchez-Granero, Miguel Ángel |
| Trinidad Segovia, Juan Evangelista |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2019. |
| Publication |
Cham : Springer International Publishing , 2019. |
| Physical Details |
XVII, 204 pages : 31 illus., 25 illus. in color. : online resource. |
| Series |
SEMA SIMAI Springer series ; 19 |
| ISBN |
9783030166458 |
| Summary Note |
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-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.: |
| Contents note |
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. |
| System details note |
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-16645-8 |
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