IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v31y2018i1d10.1007_s10959-016-0704-6.html
   My bibliography  Save this article

Spatial Central Limit Theorem for Supercritical Superprocesses

Author

Listed:
  • Piotr Miłoś

Abstract

We consider a measure-valued diffusion (i.e., a superprocess). It is determined by a couple $$(L,\psi )$$ ( L , ψ ) , where L is the infinitesimal generator of a strongly recurrent diffusion in $$\mathbb {R}^{d}$$ R d and $$\psi $$ ψ is a branching mechanism assumed to be supercritical. Such processes are known, see for example, (Englander and Winter in Ann Inst Henri Poincaré 42(2):171–185, 2006), to fulfill a law of large numbers for the spatial distribution of the mass. In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition” of the local growth induced by branching and global smoothing due to the strong recurrence of L. We also prove that the spatial fluctuations are asymptotically independent of the fluctuations of the total mass of the process.

Suggested Citation

  • Piotr Miłoś, 2018. "Spatial Central Limit Theorem for Supercritical Superprocesses," Journal of Theoretical Probability, Springer, vol. 31(1), pages 1-40, March.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0704-6
    DOI: 10.1007/s10959-016-0704-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-016-0704-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-016-0704-6?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. Radosław Adamczak & Piotr Miłoś, 2014. "$$U$$ U -Statistics of Ornstein–Uhlenbeck Branching Particle System," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1071-1111, December.
    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.

      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:31:y:2018:i:1:d:10.1007_s10959-016-0704-6. 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.