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: ENTROPIES AND FRACTIONALITY
    sub title: entropy functionals, small deviations, related integral equations
  name:
    name part: Mishura, I︠U︡lii︠a︡ S.
    role:
      role term: creator
  name:
    name part: Taylor & Francis
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: xx
    place:
      place term: S.l.]
    publisher: CHAPMAN & HALL CRC
    date issued: 2026
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: Entropies and Fractionality: Entropy Functionals, Small Deviations and Related Integral Equations starts with a systematization and calculation of various entropies (Shannon, Rnyi, and some others) of selected absolutely continuous probability distributions. The properties of the entropies are analyzed. Subsequently, a related problem is addressed: the computation and investigation of the properties of the entropic risk measure, Entropic Value-at-Risk (EVaR).Next, the book computes and compares entropy values for the one-dimensional distributions of various fractional Gaussian processes. Special attention is then given to fractional Gaussian noise, where the authors conduct a detailed analysis of the properties and asymptotic behavior of Shannon entropy. Additionally, two alternative entropy functionals are introduced which are more suitable for analytical investigation.Furthermore, relative entropy functionals for the sum of two independent Wiener processes with drift are considered, and their minimization and maximization are explored. A similar problem is addressed for a mixed fractional Brownian motion (i.e., the sum of a Wiener process and a fractional Brownian motion) with drift. The entropy minimization problem is reduced to a Fredholm integral equation of the second kind, and its unique solvability is thoroughly investigated.In the final part of the book, the optimization of small deviations for mixed fractional Brownian motion with trend is studied. This problem is closely related to the minimization of relative entropy functionals and is solved using similar techniques and results, which leads to the same class of integral equations. Since solving such equations is challenging due to the presence of an additional singularity in the kernel, efficient numerical methods have been developed to address this difficulty.Features Useful both for mathematicians interested in problems related to entropy and for practitioners, especially specialists in physics, finan…
  subject:
    topic: Topological entropy
  subject:
    topic: Functionals
  subject:
    topic: Entropie topologique
  subject:
    topic: Fonctionnelles
  classification: QA611.5
  classification: 515/.42
  related item:
    identifier: (OCoLC)1514660736
  identifier: 9781040422489
  identifier: 1040422489
  identifier: 9781003641094
  identifier: 1003641091
  identifier: 9781040422458
  identifier: 1040422454
  identifier: 1041074786
  identifier: 9781041074786
  identifier: 9781003641094 Taylor & Francis
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: YDX
    record creation date: 250731
    record change date: 20251212172420.2
    record identifier: in00005672507
    language of cataloging:
      language term: eng