Rate of growth of a transient cookie random walk

  title={Rate of growth of a transient cookie random walk},
  author={Anne-Laure Basdevant and Arvind Singh},
We consider a one-dimensional transient cookie random walk. It is known from a previous paper [3] that a cookie random walk (Xn) has positive or zero speed according to some positive parameter α > 1 or ≤ 1. In this article, we give the exact rate of growth of (Xn) in the zero speed regime, namely: for 0 < α < 1, Xn/n α+1 2 converges in law to a Mittag-Leffler distribution whereas for α = 1, Xn(log n)/n converges in probability to some positive constant. 

From This Paper

Figures, tables, and topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 19 references

A critical Galton-Watson branching process with emigration

  • V. A. Vatutin
  • Teor. Verojatnost. i Primenen., 22(3):482–497
  • 1977
Highly Influential
8 Excerpts

On the speed of a cookie random walk

  • A.-L. Basdevant, A. Singh
  • Probab . Theory Related Fields . math
  • 2006
Highly Influential
9 Excerpts

Branching processes

  • V. A. Vatutin, A. M. Zubkov
  • II. J. Soviet Math., 67(6):3407–3485
  • 1993
Highly Influential
3 Excerpts

On a critical Galton-Watson branching process with emigration

  • G. V. Vinokurov
  • Teor. Veroyatnost. i Primenen. (English…
  • 1987
Highly Influential
4 Excerpts

A critical branching process with stationary-limiting distribution

  • G. P. Yanev, N. M. Yanev
  • Stochastic Anal. Appl., 22(3):721–738
  • 2004
2 Excerpts

Similar Papers

Loading similar papers…