Fractal Dimension for Fractal Structures is popular PDF and ePub book, written by Manuel Fernández-Martínez in 2019-04-23, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Fractal Dimension for Fractal Structures can be Read Online from any device for your convenience.
Fractal Dimension for Fractal Structures Book PDF Summary
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.
Detail Book of Fractal Dimension for Fractal Structures PDF
- Author : Manuel Fernández-Martínez
- Release : 23 April 2019
- Publisher : Springer
- ISBN : 9783030166458
- Genre : Mathematics
- Total Page : 204 pages
- Language : English
- PDF File Size : 10,8 Mb
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