{"product_id":"fractal-dimension-for-fractal-structures-9783030166458","title":"Fractal Dimension for Fractal Structures","description":"\u003cp\u003eThis 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 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.\u003c\/p\u003e","brand":"Gardners","offers":[{"title":"Default Title","offer_id":52915001491735,"sku":null,"price":12146.62,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0679\/6918\/8119\/files\/9783030166458.jpg?v=1781512248","url":"https:\/\/payment.letskitaboo.com\/products\/fractal-dimension-for-fractal-structures-9783030166458","provider":"Kitaboo One eStore","version":"1.0","type":"link"}