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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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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.

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Acknowledgments

I am grateful to an anonymous referee for his/her helpful suggestions and careful reading of the manuscript. I also thank Vladimir Vatutin for sending me the paper Eppel [15].

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Authors and Affiliations

  1. Département de Mathématiques, Université Paris 13, Sorbonne Paris Cité, LAGA (CNRS UMR 7539), 93430 , Villetaneuse, France

    Yueyun Hu

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  1. Yueyun Hu
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Correspondence to Yueyun Hu.

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Research partially supported by ANR 2010 BLAN 0125.

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Hu, Y. The Almost Sure Limits of the Minimal Position and the Additive Martingale in a Branching Random Walk. J Theor Probab 28, 467–487 (2015). https://doi.org/10.1007/s10959-013-0494-z

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