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1-stable fluctuation of the derivative martingale of branching random walk

Author

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  • Hou, Haojie
  • Ren, Yan-Xia
  • Song, Renming

Abstract

In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et al. (2021) and is the branching random walk counterpart of the main result of Maillard and Pain (2019) for branching Brownian motion.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:spapps:v:172:y:2024:i:c:s0304414924000449
    DOI: 10.1016/j.spa.2024.104338
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    References listed on IDEAS

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    1. Yang, Ting & Ren, Yan-Xia, 2011. "Limit theorem for derivative martingale at criticality w.r.t branching Brownian motion," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 195-200, February.
    2. 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.
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