IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-540-74496-2_4.html

Minimal Errors for Strong and Weak Approximation of Stochastic Differential Equations

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

Author

Listed:
  • Thomas Müller-Gronbach

    (Fern Universität Hagen, Fakultät für Mathematik und Informatik)

  • Klaus Ritter

    (Technische Universität Darmstadt, Fachbereich Mathematik)

Abstract

Summary We present a survey of results on minimal errors and optimality of algorithms for strong and weak approximation of systems of stochastic differential equations. For strong approximation, emphasis lies on the analysis of algorithms that are based on point evaluations of the driving Brownian motion and on the impact of non-commutativity, if present. Furthermore, we relate strong approximation to weighted integration and reconstruction of Brownian motion, and we demonstrate that the analysis of minimal errors leads to new algorithms that perform asymptotically optimal. In particular, these algorithms use a path-dependent step-size control. for weak approximation we consider the problem of computing the expected value of a functional of the solution, and we concentrate on recent results for a worst-case analysis either with respect to the functional or with respect to the coefficients of the system. Moreover, we relate weak approximation problems to average Kolmogorov widths and quantization numbers as well as to high-dimensional tensor product problems.

Suggested Citation

  • Thomas Müller-Gronbach & Klaus Ritter, 2008. "Minimal Errors for Strong and Weak Approximation of Stochastic Differential Equations," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 53-82, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_4
    DOI: 10.1007/978-3-540-74496-2_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-540-74496-2_4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.