Fractal Dimension for Fractal Structures With Applications to Finance
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 whe...
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| Autor Corporativo: | |
| Otros Autores: | , , |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing
2019.
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| Edición: | 1st ed |
| Colección: | Springer eBooks.
SEMA SIMAI Springer Series ; 19. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b39906516*spi |
| Sumario: | 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. |
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| Descripción Física: | XVII, 204 p. : 31 il., 25 il. col |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9783030166458 |
