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: Brownian Motion, Martingales, and Stochastic Calculus
  name:
    name part: Le Gall, Jean-François.
    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: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 273 p. 5 illus., 1 illus. in color. online resource.
  abstract: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
  table of contents: Gaussian variables and Gaussian processes -- Brownian motion -- Filtrations and martingales -- Continuous semimartingales -- Stochastic integration -- General theory of Markov processes -- Brownian motion and partial differential equations -- Stochastic differential equations -- Local times -- The monotone class lemma -- Discrete martingales -- References.
  note: by Jean-François Le Gall.
  subject:
    topic: Mathematics
  subject:
    topic: Measure theory
  subject:
    topic: Economics, Mathematical
  subject:
    topic: System theory
  subject:
    topic: Mathematical models
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Quantitative Finance
  subject:
    topic: Measure and Integration
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Systems Theory, Control
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Graduate Texts in Mathematics, 274
  identifier: 9783319310893
  identifier: http://dx.doi.org/10.1007/978-3-319-31089-3
  record info:
    record creation date: 160428
    record change date: 20160708143340.0
    record identifier: 978-3-319-31089-3