Fractal Dimension for Fractal Structures With Applications to Finance
tarafından
Fernández-Martínez, Manuel. author.
Başlık
:
Fractal Dimension for Fractal Structures With Applications to Finance
Yazar
:
Fernández-Martínez, Manuel. author.
ISBN
:
9783030166458
Yazar
:
Fernández-Martínez, Manuel. author.
Edisyon
:
1st ed. 2019.
Fiziksel Niteleme
:
XVII, 204 p. 31 illus., 25 illus. in color. online resource.
Seri
:
SEMA SIMAI Springer Series, 19
İçindekiler
:
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.
Özet
:
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.
Konu Başlığı
:
Dynamics.
Ergodic theory.
Topology.
Measure theory.
Probabilities.
Algorithms.
Computer science—Mathematics.
Computer mathematics.
Dynamical Systems and Ergodic Theory. https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
Topology. https://scigraph.springernature.com/ontologies/product-market-codes/M28000
Measure and Integration. https://scigraph.springernature.com/ontologies/product-market-codes/M12120
Probability Theory and Stochastic Processes. https://scigraph.springernature.com/ontologies/product-market-codes/M27004
Algorithms. https://scigraph.springernature.com/ontologies/product-market-codes/M14018
Mathematical Applications in Computer Science. https://scigraph.springernature.com/ontologies/product-market-codes/M13110
Yazar Ek Girişi
:
García Guirao, Juan Luis.
Sánchez-Granero, Miguel Ángel.
Trinidad Segovia, Juan Evangelista.
Ek Kurum Yazar
:
SpringerLink (Online service)
Elektronik Erişim
:
Materyal Türü | Barkod | Yer Numarası | Durumu/İade Tarihi |
---|
Electronic Book | 428538-1001 | QA313 | Springer E-Book Collection |