IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-031-75023-6_6.html
   My bibliography  Save this book chapter

Extremes of Solutions of Stochastic Differential Equations by Finite Dimensional (FD) Models

In: Numerical Methods for Extreme Responses of Dynamical Systems

Author

Listed:
  • Mircea D. Grigoriu

    (Cornell University)

Abstract

Numerical methods are developed for characterizing extreme responses of dynamical systems to colored and white random inputs. System responses are solutions of stochastic differential equations (SDEs), i.e., deterministic differential equations with random inputs and/or initial conditions. The system FD responses are solutions of these equations to inputs described by the FD models constructed in the previous chapter. Conditions are established under which the distributions of extremes of system responses can be approximated by the distributions of corresponding FD responses. The conditions are essential since most of the stochastic problems have to be solved numerically, numerical methods can only solve finite dimensional problems, i.e., problems involving finite sets of random variables, and continuous-time processes are uncountable families of random variables.

Suggested Citation

  • Mircea D. Grigoriu, 2025. "Extremes of Solutions of Stochastic Differential Equations by Finite Dimensional (FD) Models," Springer Books, in: Numerical Methods for Extreme Responses of Dynamical Systems, chapter 0, pages 215-282, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-75023-6_6
    DOI: 10.1007/978-3-031-75023-6_6
    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:978-3-031-75023-6_6. 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.