IDEAS home Printed from https://ideas.repec.org/h/wsi/wschap/9789812564528_0007.html
   My bibliography  Save this book chapter

The Mathematics of Hypermodels

In: Hypermodels In Mathematical Finance Modelling via Infinitesimal Analysis

Author

Listed:
  • Siu-Ah Ng

    (School of Mathematical, Stats & IT, University Natal-Pietermaritzburg, South Africa)

Abstract

The following sections are included:Mathematical logic and Classical HyperanalysisLogic and hypermodels *ℝConstruction of *ℝ using the compactness theoremConstruction *ℝ using ultrapowersSome basic properties of hypermodel *ℝHypermodels of ℝ in richer languagesSome examplesReferencesThe hyperuniverseDoing mathematics in the languages of set theoryHyperuniverse and the hyperextensionThe existence of the hyperextensionApplications and examplesReferencesHyperanalysis of probabilityThe Loeb measure constructionLoeb integration theorySome examplesHypermodels of Brownian MotionAnderson's discrete hypermodel of Brownian motionSome *continuous hypermodels of Brownian motionSome examplesItô Integral and Stochastic Differential EquationsSome general remarksWiener integral and Itô integralItô's lemma and the Stratonovitch integralSolving Stochastic differential equationsMalliavin calculusWhite noise analysisUniversality and homogeneity properties of hyperfinite models

Suggested Citation

  • Siu-Ah Ng, 2003. "The Mathematics of Hypermodels," World Scientific Book Chapters, in: Hypermodels In Mathematical Finance Modelling via Infinitesimal Analysis, chapter 7, pages 121-255, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812564528_0007
    as

    Download full text from publisher

    File URL: https://www.worldscientific.com/doi/pdf/10.1142/9789812564528_0007
    Download Restriction: Ebook Access is available upon purchase.

    File URL: https://www.worldscientific.com/doi/abs/10.1142/9789812564528_0007
    Download Restriction: Ebook Access is available upon purchase.
    ---><---

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

    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:wsi:wschap:9789812564528_0007. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/page/worldscibooks .

    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.