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Limit distributions for minimal displacement of branching random walks
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  • Published: September 1991

Limit distributions for minimal displacement of branching random walks

  • F. M. Dekking1 &
  • B. Host2 

Probability Theory and Related Fields volume 90, pages 403–426 (1991)Cite this article

  • 265 Accesses

  • 31 Citations

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Summary

We study the minimal displacement (X n ) of branching random walk with non-negative steps. It is shown that (X n −EX n ) is tight under a mild moment condition on the displacements. For supercritical B.R.W. (X n ) converges almost surely. For critical B.R.W. we determine the possible limit points of (X n −EX n ), and we prove a generalization of Kolmogorov's theorem on the extinction probability of a critical branching process. Finally we generalize Bramson's results on the almost sure convergence ofX n log 2/log logn.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Informatics, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    F. M. Dekking

  2. Département de Mathématique et Informatique, Faculté des Sciences de Luminy, 163 avenue de Luminy, F-13288, Marseille Cedex 9, France

    B. Host

Authors
  1. F. M. Dekking
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  2. B. Host
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Cite this article

Dekking, F.M., Host, B. Limit distributions for minimal displacement of branching random walks. Probab. Th. Rel. Fields 90, 403–426 (1991). https://doi.org/10.1007/BF01193752

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  • Received: 12 June 1990

  • Revised: 24 April 1991

  • Issue Date: September 1991

  • DOI: https://doi.org/10.1007/BF01193752

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Keywords

  • Stochastic Process
  • Random Walk
  • Probability Theory
  • Mathematical Biology
  • Limit Point
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