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Record Nr. |
UNINA9910338254303321 |
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Autore |
Fernández-Martínez Manuel |
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Titolo |
Fractal Dimension for Fractal Structures : With Applications to Finance / / by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
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ISBN |
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Edizione |
[1st ed. 2019.] |
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Descrizione fisica |
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1 online resource (217 pages) |
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Collana |
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SEMA SIMAI Springer Series, , 2199-3041 ; ; 19 |
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Disciplina |
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Soggetti |
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Dynamics |
Ergodic theory |
Topology |
Measure theory |
Probabilities |
Algorithms |
Computer science—Mathematics |
Computer mathematics |
Dynamical Systems and Ergodic Theory |
Measure and Integration |
Probability Theory and Stochastic Processes |
Mathematical Applications in Computer Science |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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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