Transience and Recurrence of Certain State Dependent Branching Processes.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Let X sub n denote the Galton-Watson branching process with the following modifications Whenever X sub n 0, X subn 1 is drawn from a fixed immigration distribution. Whenever X sub n 1 i and i not equal 0, either 1 a deterministic non-random number ki of individuals are removed or made sterile, or 2 each individual is independently subject to removal or sterility with probability zeta i, before branching reproduction occurs. Conditions on ki, zetai are presented which are sufficient for transience, recurrence, and positive-recurrence of X sub n.
- Statistics and Probability