IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v17y2004i2d10.1023_bjotp.0000020704.68569.25.html
   My bibliography  Save this article

Tanaka Formulae for (α, d, β)-Superprocesses

Author

Listed:
  • L. Mytnik

    (Faculty of Industrial Engineering and Management)

  • K.-N. Xiang

    (Hunan Normal University)

Abstract

We establish Tanaka like formulae for the local time of (α, d, β)-superprocess in the dimensions where the local time exists. The result generalizes the result of Adler, Lewin who proved existence of Tanaka formulae for a class of super-processes with finite variance. The fact that we abandon the finite variance assumption, requires using an L 1+θ convergence argument (with 0

Suggested Citation

  • L. Mytnik & K.-N. Xiang, 2004. "Tanaka Formulae for (α, d, β)-Superprocesses," Journal of Theoretical Probability, Springer, vol. 17(2), pages 483-502, April.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020704.68569.25
    DOI: 10.1023/B:JOTP.0000020704.68569.25
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/B:JOTP.0000020704.68569.25
    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.0000020704.68569.25?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. Leonid Mytnik, 1998. "Collision Measure and Collision Local Time for (α, d, β) Superprocesses," Journal of Theoretical Probability, Springer, vol. 11(3), pages 733-763, July.
    2. Adler, Robert J. & Lewin, Marica, 1992. "Local time and Tanaka formulae for super Brownian and super stable processes," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 45-67, May.
    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. Krone, Stephen M., 1997. "Representations for continuous additive functionals of super-Brownian and super-stable processes," Statistics & Probability Letters, Elsevier, vol. 34(3), pages 211-223, June.
    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. Hambly, Ben & Koepernik, Peter, 2023. "Dimension results and local times for superdiffusions on fractals," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 377-417.
    4. Feldman, Raisa E. & Iyer, Srikanth K., 1996. "A representation for functionals of superprocesses via particle picture," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 173-186, November.
    5. Kaj, I. & Salminen, P., 1995. "On the ultimate value of local time of one-dimensional super-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 21-42, September.
    6. Ethier, S. N. & Krone, Stephen M., 1995. "Comparing Fleming-Viot and Dawson-Watanabe processes," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 171-190, December.
    7. Bojdecki, Tomasz & Talarczyk, Anna, 2005. "Particle picture approach to the self-intersection local time of density processes in," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 449-479, March.
    8. Dawson, D.A. & Vaillancourt, J. & Wang, H., 2021. "Joint Hölder continuity of local time for a class of interacting branching measure-valued diffusions," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 212-233.

    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.0000020704.68569.25. 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.