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: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
  name:
    name part: Kruse, Raphael.
    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: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 177 p. 4 illus. online resource.
  abstract: In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
  table of contents: Introduction -- Stochastic Evolution Equations in Hilbert Spaces -- Optimal Strong Error Estimates for Galerkin Finite Element Methods -- A Short Review of the Malliavin Calculus in Hilbert Spaces -- A Malliavin Calculus Approach to Weak Convergence -- Numerical Experiments -- Some Useful Variations of Gronwall’s Lemma -- Results on Semigroups and their Infinitesimal Generators -- A Generalized Version of Lebesgue’s Theorem -- References -- Index.
  note: by Raphael Kruse.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Numerical analysis
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Numerical Analysis
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Partial Differential Equations
  classification: QA297-299.4
  classification: 518
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2093
  identifier: 9783319022314
  identifier: http://dx.doi.org/10.1007/978-3-319-02231-4
  record info:
    record creation date: 131114
    record change date: 20151103131817.0
    record identifier: 978-3-319-02231-4