IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v146y2022icp311-334.html
   My bibliography  Save this article

Extensions of Bougerol’s identity in law and the associated anticipative path transformations

Author

Listed:
  • Hariya, Yuu

Abstract

Let B={Bt}t≥0 be a one-dimensional standard Brownian motion and denote by At,t≥0, the quadratic variation of the geometric Brownian motion eBt,t≥0. Bougerol’s celebrated identity in law (1983) asserts that, if β={β(t)}t≥0 is another Brownian motion independent of B, then, for every fixed t>0, β(At) is identical in law with sinhBt. In this paper, we extend Bougerol’s identity to an identity in law for processes up to time t, which exhibits a certain invariance of the law of Brownian motion. The extension is described in terms of anticipative transforms of B involving At as an anticipating factor. A Girsanov-type formula for those transforms is shown. An extension of a variant of Bougerol’s identity is also presented.

Suggested Citation

  • Hariya, Yuu, 2022. "Extensions of Bougerol’s identity in law and the associated anticipative path transformations," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 311-334.
    • Handle: RePEc:eee:spapps:v:146:y:2022:i:c:p:311-334
    DOI: 10.1016/j.spa.2022.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000059
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.01.005?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. Hariya, Yuu, 2020. "On some identities in law involving exponential functionals of Brownian motion and Cauchy random variable," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5999-6037.
    Full references (including those not matched with items on IDEAS)

    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. Yuu Hariya, 2022. "Integral Representations for the Hartman–Watson Density," Journal of Theoretical Probability, Springer, vol. 35(1), pages 209-230, March.

    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:spapps:v:146:y:2022:i:c:p:311-334. 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.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.