IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v31y2018i2d10.1007_s10959-016-0736-y.html
   My bibliography  Save this article

Central Limit Theorems for Supercritical Superprocesses with Immigration

Author

Listed:
  • Li Wang

    (Beijing University of Chemical Technology)

Abstract

In this paper, we establish a central limit theorem for a large class of general supercritical superprocesses with immigration with spatially dependent branching mechanisms satisfying a second moment condition. This central limit theorem extends and generalizes the results obtained by Ren et al. (Stoch Process Appl 125:428–457, 2015). We first give laws of large numbers for supercritical superprocesses with immigration since there are few convergence results on immigration superprocesses, then based on these results, we establish the central limit theorem.

Suggested Citation

  • Li Wang, 2018. "Central Limit Theorems for Supercritical Superprocesses with Immigration," Journal of Theoretical Probability, Springer, vol. 31(2), pages 984-1012, June.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:2:d:10.1007_s10959-016-0736-y
    DOI: 10.1007/s10959-016-0736-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-016-0736-y
    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/s10959-016-0736-y?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. Li Wang, 2010. "An Almost Sure Limit Theorem for Super-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(2), pages 401-416, June.
    2. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.
    3. El Karoui, Nicole & Roelly, Sylvie, 1991. "Propriétés de martingales, explosion et représentation de Lévy--Khintchine d'une classe de processus de branchement à valeurs mesures," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 239-266, August.
    4. Li, Zeng-Hu, 1992. "Measure-valued branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 249-264, December.
    5. Li, Zeng-Hu, 1996. "Immigration structures associated with Dawson-Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 73-86, 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. Wenming Hong, 2003. "Large Deviations for the Super-Brownian Motion with Super-Brownian Immigration," Journal of Theoretical Probability, Springer, vol. 16(4), pages 899-922, October.
    2. Hong, Wenming, 2002. "Longtime behavior for the occupation time process of a super-Brownian motion with random immigration," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 43-62, November.
    3. Liu, Rongli & Ren, Yan-Xia & Song, Renming, 2022. "Convergence rate for a class of supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 286-327.
    4. Hong, Wenming & Li, Zenghu, 2001. "Fluctuations of a super-Brownian motion with randomly controlled immigration," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 285-291, February.
    5. Li, Zenghu & Zhang, Mei, 2006. "Fluctuation limit theorems of immigration superprocesses with small branching," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 401-411, February.
    6. Li, Zeng-Hu, 1996. "Immigration structures associated with Dawson-Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 73-86, March.
    7. Leduc, Guillaume, 2006. "Martingale problem for superprocesses with non-classical branching functional," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1468-1495, October.
    8. Xiong, Jie & Yang, Xu, 2016. "Superprocesses with interaction and immigration," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3377-3401.
    9. Mandler, Christian & Overbeck, Ludger, 2022. "A functional Itō-formula for Dawson–Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 202-228.
    10. Kyprianou, A.E. & Ren, Y.-X., 2012. "Backbone decomposition for continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 139-144.
    11. Zenghu Li & Chunhua Ma, 2008. "Catalytic Discrete State Branching Models and Related Limit Theorems," Journal of Theoretical Probability, Springer, vol. 21(4), pages 936-965, December.
    12. He, Hui, 2009. "Discontinuous superprocesses with dependent spatial motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 130-166, January.
    13. Dawson, Donald A. & Hochberg, Kenneth J. & Vinogradov, Vladimir, 1996. "High-density limits of hierarchically structured branching-diffusing populations," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 191-222, July.
    14. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2015. "Central limit theorems for supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 428-457.
    15. Liu, Rongli & Ren, Yan-Xia & Song, Renming & Sun, Zhenyao, 2023. "Subcritical superprocesses conditioned on non-extinction," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 498-534.

    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:2:d:10.1007_s10959-016-0736-y. 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.