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Fractal dimension for fractal struct...

Fernandez-Martinez, Manuel.

Fractal dimension for fractal structureswith applications to finance /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fractal dimension for fractal structuresby Manuel Fernandez-Martinez ... [et al.].
Reminder of title:	with applications to finance /
other author:	Fernandez-Martinez, Manuel.
Published:	Cham :Springer International Publishing :2019.
Description:	xvii, 204 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Fractal analysis.
Online resource:	https://doi.org/10.1007/978-3-030-16645-8
ISBN:	9783030166458$q(electronic bk.)

Fractal dimension for fractal structureswith applications to finance /
Fractal dimension for fractal structureswith applications to finance /[electronic resource] :by Manuel Fernandez-Martinez ... [et al.]. - Cham :Springer International Publishing :2019. - xvii, 204 p. :ill., digital ;24 cm. - SEMA SIMAI Springer series,v.192199-3041 ;. - SEMA SIMAI Springer series ;v.4..

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 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.

ISBN: 9783030166458$q(electronic bk.)

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

675575
Fractal analysis.

LC Class. No.: QA614.86

Dewey Class. No.: 514.742

Fractal dimension for fractal structureswith applications to finance /
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245 0 0 $a Fractal dimension for fractal structures $h [electronic resource] : $b with applications to finance / $c by Manuel Fernandez-Martinez ... [et al.].
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505 0 $a 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.
520 $a 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.
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