Probability Theory and Related Fields

, Volume 90, Issue 3, pp 403–426

Limit distributions for minimal displacement of branching random walks

Authors

  • F. M. Dekking
    • Department of Mathematics and InformaticsDelft University of Technology
  • B. Host
    • Département de Mathématique et InformatiqueFaculté des Sciences de Luminy
Article

DOI: 10.1007/BF01193752

Cite this article as:
Dekking, F.M. & Host, B. Probab. Th. Rel. Fields (1991) 90: 403. doi:10.1007/BF01193752

Summary

We study the minimal displacement (Xn) of branching random walk with non-negative steps. It is shown that (XnEXn) is tight under a mild moment condition on the displacements. For supercritical B.R.W. (Xn) converges almost surely. For critical B.R.W. we determine the possible limit points of (XnEXn), 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 ofXn log 2/log logn.

Copyright information

© Springer-Verlag 1991