IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v38y1995i1p7-11.html
   My bibliography  Save this article

A basis for iterated stochastic integrals

Author

Listed:
  • Gaines, J.G.

Abstract

We explore the algebra of the sets of iterated Stratonovich or Ito integrals that appear in the stochastic Taylor series expansion of the solution to a stochastic differential equation. The algebra of iterated Stratonovich integrals with pointwise multiplication is a shuffle algebra, allowing us to apply results from work on shuffle algebras. The pointwise product of Ito integrals is a modified shuffle product. Lyndon words provide an algebraic basis for both sets of iterated integrals. This basis is similar to, but simpler than, that obtained by Sussmann using Hall words.

Suggested Citation

  • Gaines, J.G., 1995. "A basis for iterated stochastic integrals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 7-11.
    • Handle: RePEc:eee:matcom:v:38:y:1995:i:1:p:7-11
    DOI: 10.1016/0378-4754(93)E0061-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378475493E00619
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/0378-4754(93)E0061-9?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.

    References listed on IDEAS

    as
    1. P. E. Kloeden & Eckhard Platen, 1991. "Stratonovich and Ito Stochastic Taylor Expansions," Published Paper Series 1991-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tocino, A., 2009. "Multiple stochastic integrals with Mathematica," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1658-1667.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Castell, Fabienne & Gaines, Jessica, 1995. "An efficient approximation method for stochastic differential equations by means of the exponential Lie series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 13-19.
    2. Frezza, Massimiliano, 2012. "Modeling the time-changing dependence in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1510-1520.
    3. Yan, Sizhe & Wang, Weiqing & Li, Xiaozhu & Maimaiti, Pakezhati & Zhao, Yi, 2024. "Cross-regional green certificate transaction strategies based on a double-layer game model," Applied Energy, Elsevier, vol. 356(C).

    More about this item

    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:eee:matcom:v:38:y:1995:i:1:p:7-11. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.