Hidden Bibliographic Details
| Other authors / contributors: | García Guirao, Juan Luis, author.
Sánchez-Granero, Miguel Ángel, author.
Trinidad Segovia, Juan Evangelista, author.
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| ISBN: | 9783030166458
3030166457
3030166449
9783030166441
9783030166465
3030166465
9783030166472
3030166473
9783030166441
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| Digital file characteristics: | text file PDF
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| Notes: | Online resource; title from PDF title page (EBSCO, viewed April 25, 2019).
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| Summary: | 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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| Other form: | Printed edition: 9783030166441
Printed edition: 9783030166465
Printed edition: 9783030166472
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| Standard no.: | 10.1007/978-3-030-16645-8
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