IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v17y2004i2d10.1023_bjotp.0000020698.51262.24.html
   My bibliography  Save this article

Tanaka Formula for Multidimensional Brownian Motions

Author

Listed:
  • H. Uemura

    (Aichi University of Education)

Abstract

We study the Tanaka formula for multidimensional Brownian motions in the framework of generalized Wiener functionals. More precisely, we show that the submartingale U(B t −x) is decomposed in the sence of generalized Wiener functionals into the sum of a martingale and the Brownian local time, U being twice of the kernel of Newtonian potential and B t the multidimensional Brownian motion. We also discuss on an aspect of the Tanaka formula for multidimensional Brownian motions as the Doob–Meyer decomposition.

Suggested Citation

  • H. Uemura, 2004. "Tanaka Formula for Multidimensional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 17(2), pages 347-366, April.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020698.51262.24
    DOI: 10.1023/B:JOTP.0000020698.51262.24
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTP.0000020698.51262.24
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/B:JOTP.0000020698.51262.24?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. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
    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. Yan, Litan & Shen, Guangjun, 2010. "On the collision local time of sub-fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 296-308, March.
    2. Bojdecki, Tomasz & Gorostiza, Luis G., 1995. "Self-intersection local time for Gaussian '(d)-processes: Existence, path continuity and examples," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 191-226, December.
    3. Uemura, H., 2008. "Generalized positive continuous additive functionals of multidimensional Brownian motion and their associated Revuz measures," Stochastic Processes and their Applications, Elsevier, vol. 118(10), pages 1870-1891, October.
    4. Rudenko, Alexey, 2012. "Some properties of the Itô–Wiener expansion of the solution of a stochastic differential equation and local times," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2454-2479.
    5. Marie F. Kratz & José R. León, 2001. "Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields," Journal of Theoretical Probability, Springer, vol. 14(3), pages 639-672, July.
    6. Franco Flandoli & Peter Imkeller & Ciprian A. Tudor, 2014. "2D-Stochastic Currents over the Wiener Sheet," Journal of Theoretical Probability, Springer, vol. 27(2), pages 552-575, June.
    7. Albeverio, Sergio & Hu, Yaozhong & Zhou, Xian Yin, 1997. "A remark on non-smoothness of the self-intersection local time of planar Brownian motion," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 57-65, February.
    8. Naitzat, Gregory & Adler, Robert J., 2017. "A central limit theorem for the Euler integral of a Gaussian random field," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 2036-2067.
    9. Shi, Qun & Yu, Xianye, 2017. "Fractional smoothness of derivative of self-intersection local times," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 241-251.

    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:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020698.51262.24. 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: 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.