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The Almost Sure Limits of the Minimal Position and the Additive Martingale in a Branching Random Walk

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  • Yueyun Hu

    (Université Paris 13)

Abstract

Consider a real-valued branching random walk in the boundary case. Using the techniques developed by Aïdékon and Shi (2012), we give two integral tests which describe, respectively, the lower limits for the minimal position and the upper limits for the associated additive martingale.

Suggested Citation

  • Yueyun Hu, 2015. "The Almost Sure Limits of the Minimal Position and the Additive Martingale in a Branching Random Walk," Journal of Theoretical Probability, Springer, vol. 28(2), pages 467-487, June.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:2:d:10.1007_s10959-013-0494-z
    DOI: 10.1007/s10959-013-0494-z
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    References listed on IDEAS

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    1. Chauvin, Brigitte & Rouault, Alain & Wakolbinger, Anton, 1991. "Growing conditioned trees," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 117-130, October.
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    Cited by:

    1. Hou, Haojie & Ren, Yan-Xia & Song, Renming, 2024. "1-stable fluctuation of the derivative martingale of branching random walk," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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