rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Fractal Dimension for Fractal Structures
    sub title: With Applications to Finance
  name:
    name part: Fernández-Martínez, Manuel.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: García Guirao, Juan Luis.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Sánchez-Granero, Miguel Ángel.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Trinidad Segovia, Juan Evangelista.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 204 p. 31 illus., 25 illus. in color. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Manuel Fernández-Martínez, Juan Luis García Guirao, Miguel Ángel Sánchez-Granero, Juan Evangelista Trinidad Segovia.
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Topology
  subject:
    topic: Measure theory
  subject:
    topic: Probabilities
  subject:
    topic: Algorithms
  subject:
    topic: Computer science-Mathematics
  subject:
    topic: Computer mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Topology
  subject:
    topic: Measure and Integration
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Algorithms
  subject:
    topic: Mathematical Applications in Computer Science
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SEMA SIMAI Springer Series, 19
  identifier: 9783030166458
  identifier: https://doi.org/10.1007/978-3-030-16645-8
  record info:
    record creation date: 190423
    record change date: 20191022062124.0
    record identifier: 978-3-030-16645-8