IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v120y2010i10p2064-2077.html
   My bibliography  Save this article

Upper large deviations of branching processes in a random environment--Offspring distributions with geometrically bounded tails

Author

Listed:
  • Böinghoff, Christian
  • Kersting, Götz

Abstract

We generalize a result by Kozlov on large deviations of branching processes (Zn) in an i.i.d. random environment. Under the assumption that the offspring distributions have geometrically bounded tails and mild regularity of the associated random walk S, the asymptotics of is (on logarithmic scale) completely determined by a convex function [Gamma] depending on properties of S. In many cases [Gamma] is identical with the rate function of (Sn). However, if the branching process is strongly subcritical, there is a phase transition and the asymptotics of and differ for small [theta].

Suggested Citation

  • Böinghoff, Christian & Kersting, Götz, 2010. "Upper large deviations of branching processes in a random environment--Offspring distributions with geometrically bounded tails," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 2064-2077, September.
  • Handle: RePEc:eee:spapps:v:120:y:2010:i:10:p:2064-2077
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00149-3
    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.

    References listed on IDEAS

    as
    1. Afanasyev, V.I. & Geiger, J. & Kersting, G. & Vatutin, V.A., 2005. "Functional limit theorems for strongly subcritical branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1658-1676, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Nakashima, Makoto, 2013. "Lower deviations of branching processes in random environment with geometrical offspring distributions," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3560-3587.
    2. Grama, Ion & Liu, Quansheng & Miqueu, Eric, 2017. "Berry–Esseen’s bound and Cramér’s large deviation expansion for a supercritical branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1255-1281.
    3. Huang, Chunmao & Liu, Quansheng, 2012. "Moments, moderate and large deviations for a branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 522-545.

    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. Böinghoff, Christian, 2014. "Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3553-3577.
    2. Huang, Chunmao & Liu, Quansheng, 2012. "Moments, moderate and large deviations for a branching process in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 522-545.
    3. Alsmeyer, Gerold & Gröttrup, Sören, 2016. "Branching within branching: A model for host–parasite co-evolution," Stochastic Processes and their Applications, Elsevier, vol. 126(6), pages 1839-1883.
    4. Bansaye, Vincent, 2009. "Surviving particles for subcritical branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2436-2464, August.
    5. Li, Zenghu & Xu, Wei, 2018. "Asymptotic results for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 108-131.
    6. Wang, Yuejiao & Liu, Zaiming & Li, Yingqiu & Liu, Quansheng, 2017. "On the concept of subcriticality and criticality and a ratio theorem for a branching process in a random environment," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 97-103.
    7. Xu, Wei, 2023. "Asymptotics for exponential functionals of random walks," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 1-42.
    8. V. I. Afanasyev & C. Böinghoff & G. Kersting & V. A. Vatutin, 2012. "Limit Theorems for Weakly Subcritical Branching Processes in Random Environment," Journal of Theoretical Probability, Springer, vol. 25(3), pages 703-732, September.

    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:120:y:2010:i:10:p:2064-2077. 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.