IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v6y1978i3p241-252.html
   My bibliography  Save this article

A central limit theorem for martingales and an application to branching processes

Author

Listed:
  • Scott, D. J.

Abstract

A functional central limit theorem is obtained for martingales which are not uniformly asymptotically negligible but grow at a geometric rate. The function space is not the usual C[0,1] or D[0,1] but RN, the space of all real sequences and the metric used leads to a non-separable metric space. The main theorem is applied to a martingale obtained from a supercritical Galton-Watson branching process and as simple corollaries the already known central limit theorems for the Harris and Lotka-Nagaev estimators of the mean of the offspring distribution, are obtained.

Suggested Citation

  • Scott, D. J., 1978. "A central limit theorem for martingales and an application to branching processes," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 241-252, February.
    • Handle: RePEc:eee:spapps:v:6:y:1978:i:3:p:241-252
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(78)90021-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rahimov, I., 2017. "Asymptotic inference for non-supercritical partially observed branching processes," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 26-32.
    2. Arpita Inamdar & Mohan Kale, 2016. "Joint Estimation of Offspring Mean and Offspring Variance of Controlled Branching Process," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 248-268, August.
    3. Horst, Ulrich & Xu, Wei, 2021. "Functional limit theorems for marked Hawkes point measures," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 94-131.
    4. James Kuelbs & Anand N. Vidyashankar, 2011. "Weak Convergence Results for Multiple Generations of a Branching Process," Journal of Theoretical Probability, Springer, vol. 24(2), pages 376-396, June.

    More about this item

    Statistics

    Access and download statistics

    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:6:y:1978:i:3:p:241-252. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.