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

• Autore: Fernández-Martínez Manuel
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019
• Edizione: 1st ed. 2019.
• Descrizione fisica: 1 online resource (217 pages)
• Disciplina: 514.742
• Soggetto topico: 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
• Persona (resp. second.): García GuiraoJuan Luis; Sánchez-GraneroMiguel Ángel; Trinidad SegoviaJuan Evangelista
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Fractal Dimension for Fractal Structures
• ISBN: 3-030-16645-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910338254303321
• Lo trovi qui: Univ. Federico II
• Serie: SEMA SIMAI Springer Series, . 2199-3041 ; ; 19