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: Analysis of Variations for Self-similar Processes
    sub title: A Stochastic Calculus Approach
  name:
    name part: Tudor, Ciprian.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 268 p. online resource.
  abstract: Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.
  table of contents: Preface -- Introduction -- Part I Examples of Self-Similar Processes -- 1.Fractional Brownian Motion and Related Processes -- 2.Solutions to the Linear Stochastic Heat and Wave Equation -- 3.Non Gaussian Self-Similar Processes -- 4.Multiparameter Gaussian Processes -- Part II Variations of Self-Similar Process: Central and Non-Central Limit Theorems -- 5.First and Second Order Quadratic Variations. Wavelet-Type Variations -- 6.Hermite Variations for Self-Similar Processes -- Appendices: A.Self-Similar Processes with Stationary Increments: Basic Properties -- B.Kolmogorov Continuity Theorem -- C.Multiple Wiener Integrals and Malliavin Derivatives -- References -- Index.
  note: by Ciprian Tudor.
  subject:
    topic: Mathematics
  subject:
    topic: Probabilities
  subject:
    topic: Statistics
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Statistics, general
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Probability and Its Applications
  identifier: 9783319009360
  identifier: http://dx.doi.org/10.1007/978-3-319-00936-0
  record info:
    record creation date: 130805
    record change date: 20151218121842.0
    record identifier: 978-3-319-00936-0