Fractal Dimension for Fractal Structures With Applications to Finance /

• Κύριοι συγγραφείς: Fernández-Martínez, Manuel (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), García Guirao, Juan Luis (http://id.loc.gov/vocabulary/relators/aut), Sánchez-Granero, Miguel Ángel (http://id.loc.gov/vocabulary/relators/aut), Trinidad Segovia, Juan Evangelista (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Έκδοση: 1st ed. 2019.
• Σειρά: SEMA SIMAI Springer Series, 19
• Θέματα: 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.

 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. 

 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.