IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v24y2018i4p289-308n2.html
   My bibliography  Save this article

A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation

Author

Listed:
  • Yamada Toshihiro

    (Hitotsubashi University, Tokyo, Japan)

  • Yamamoto Kenta

    (MUFG Bank, Tokyo, Japan)

Abstract

This paper proposes a new Markov chain approach to second-order weak approximations of stochastic differential equations (SDEs) driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the Lévy area simulation method are not used. The required number of random variables is still d in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment-matched random variables.

Suggested Citation

  • Yamada Toshihiro & Yamamoto Kenta, 2018. "A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 289-308, December.
  • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:4:p:289-308:n:2
    DOI: 10.1515/mcma-2018-2024
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2018-2024
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/mcma-2018-2024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:bpj:mcmeap:v:24:y:2018:i:4:p:289-308:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.