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Precise estimates of presence probabilities in the branching random walk

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  • Rouault, Alain

Abstract

In the subcritical speed area of a supercritical branching random walk, we prove that when the number of generations grows the probability of presence is asymptotically proportional to the corresponding expectation as in a subcritical Galton-Watson process. This improves a known result on the logarithm of this probability. The basic tools are a discrete version of the Feynman-Kac representation and large deviations.

Suggested Citation

  • Rouault, Alain, 1993. "Precise estimates of presence probabilities in the branching random walk," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 27-39, January.
  • Handle: RePEc:eee:spapps:v:44:y:1993:i:1:p:27-39
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    Cited by:

    1. Shuxiong Zhang, 2023. "Lower Deviation Probabilities for Level Sets of the Branching Random Walk," Journal of Theoretical Probability, Springer, vol. 36(2), pages 811-844, June.
    2. Krell, N. & Rouault, A., 2011. "Martingales and rates of presence in homogeneous fragmentations," Stochastic Processes and their Applications, Elsevier, vol. 121(1), pages 135-154, January.

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