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Subcritical branching processes in a two-state random environment, and a percolation problem on trees

Published online by Cambridge University Press:  14 July 2016

F. M. Dekking
F. M. Dekking*
Affiliation:
Delft University of Technology
*
∗ Postal address: Department of Mathematics, Delft University of Technology, Julianalaan 132, 2628 BL Delft, The Netherlands.
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Abstract

We determine the decay rate of the survival probability of subcritical branching processes in a two-state random environment, where one state is subcritical, the other supercritical. This result is applied to obtain the asymptotic behavior (as n →∞) of the number of different words of length n occurring on the binary, and generally the b-ary, tree with Bernoulli percolation.

Keywords

SURVIVAL PROBABILITYBERNOULLI PERCOLATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 4 , December 1987, pp. 798 - 808
Copyright
Copyright © Applied Probability Trust 1987 

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References

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