IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v158y2023icp377-417.html
   My bibliography  Save this article

Dimension results and local times for superdiffusions on fractals

Author

Listed:
  • Hambly, Ben
  • Koepernik, Peter

Abstract

We consider the Dawson–Watanabe superprocess obtained from a spatial motion with sub-Gaussian transition densities on a metric measure space with finite Hausdorff dimension, and examine the dimensions of the range and the set of times when the support intersects a given set, generalising results of Serlet and Tribe. As intermediate results, we prove existence of local times for the superprocess if the spectral dimension of the spatial motion satisfies ds<4, and prove that (2−ds/2)∧1 is the critical Hölder-continuity exponent in the time variable. Furthermore, we prove a bound on moments of the integrated superprocess, and give uniform upper bounds on the mass the superprocess assigns to small balls, generalising a result of Perkins.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:158:y:2023:i:c:p:377-417
    DOI: 10.1016/j.spa.2023.01.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441492300008X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2023.01.008?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. 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. 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.
    4. 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.
    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:eee:spapps:v:158:y:2023:i:c:p:377-417. 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.