Fractal Dimension for Fractal Structures - With Applications to Finance (Hardcover, 1st ed. 2019)

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 Levy 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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	SEMA SIMAI Springer Series, 19
Release date:	May 2019
First published:	2019
Authors:	Manuel Fernandez-Martinez • Juan Luis Garcia Guirao • Miguel Angel Sanchez-Granero • Juan Evangelista Trinidad Segovia
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	204
Edition:	1st ed. 2019
ISBN-13:	978-3-03-016644-1
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Topology > General Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science
LSN:	3-03-016644-9
Barcode:	9783030166441

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