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:
    non sort: An
    title: Introduction to Infinite-Dimensional Analysis
  name:
    name part: Prato, Giuseppe Da.
    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: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: X, 208 p. online resource.
  abstract: In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension. Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior.
  table of contents: Gaussian measures in Hilbert spaces -- The Cameron–Martin formula -- Brownian motion -- Stochastic perturbations of a dynamical system -- Invariant measures for Markov semigroups -- Weak convergence of measures -- Existence and uniqueness of invariant measures -- Examples of Markov semigroups -- L2 spaces with respect to a Gaussian measure -- Sobolev spaces for a Gaussian measure -- Gradient systems.
  note: by Giuseppe Da Prato.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Partial Differential Equations
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783540290216
  identifier: http://dx.doi.org/10.1007/3-540-29021-4
  record info:
    record creation date: 100301
    record change date: 20151204151136.0
    record identifier: 978-3-540-29021-6