| 书目名称 | Fractal Dimension for Fractal Structures |
| 副标题 | With Applications to |
| 编辑 | Manuel Fernández-Martínez,Juan Luis García Guirao, |
| 视频video | |
| 概述 | Develops a new theory of fractal dimension using the topological concept of a fractal structure.Provides a rigorous description of the first-known (and currently, the only) general algorithm for calcu |
| 丛书名称 | SEMA SIMAI Springer Series |
| 图书封面 |  |
| 描述 | .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 algorithmsfor 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 rea |
| 出版日期 | Book 2019 |
| 关键词 | fractal; fractal structure; fractal dimension; Hausdorff dimension; Hurst exponent |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-16645-8 |
| isbn_ebook | 978-3-030-16645-8Series ISSN 2199-3041 Series E-ISSN 2199-305X |
| issn_series | 2199-3041 |
| copyright | Springer Nature Switzerland AG 2019 |
发表于 2025-3-21 17:33:32
