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Fractal Dimension for Fractal Structures = With Applications to Finance /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fractal Dimension for Fractal Structures/ by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia.
其他題名:	With Applications to Finance /
作者:	Fernández-Martínez, Manuel.
其他作者:	García Guirao, Juan Luis.
面頁冊數:	XVII, 204 p. 31 illus., 25 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Dynamics. -
電子資源:	https://doi.org/10.1007/978-3-030-16645-8
ISBN:	9783030166458

Fractal Dimension for Fractal Structures = With Applications to Finance /
Fernández-Martínez, Manuel.

Fractal Dimension for Fractal StructuresWith Applications to Finance /[electronic resource] :by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia. - 1st ed. 2019. - XVII, 204 p. 31 illus., 25 illus. in color.online resource. - SEMA SIMAI Springer Series,192199-3041 ;. - SEMA SIMAI Springer Series,5.

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.

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.

ISBN: 9783030166458

Standard No.: 10.1007/978-3-030-16645-8doiSubjects--Topical Terms:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Fractal Dimension for Fractal Structures = With Applications to Finance /
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