Fractal dimension for fractal structures : with applications to finance

• 作者： Fernandez-Martinez, Manuel, author.
• 其他作者：
  • Garcia Guirao, Juan Luis, author.
  • Sanchez-Granero, Miguel Angel, author.
  • Trinidad Segovia, Juan Evangelista, author.
  • SpringerLink (Online service)
• 其他題名：
  • SEMA SIMAI Springer series ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： SEMA SIMAI Springer series,volume 19
• 主題： Fractal analysis. , Finance--Mathematical models. , Dynamical Systems and Ergodic Theory. , Topology. , Measure and Integration. , Probability Theory and Stochastic Processes. , Algorithms. , Mathematical Applications in Computer Science.
• ISBN： 9783030166458 (electronic bk.) 、 9783030166441 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
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• 摘要註: 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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