Transience and Recurrence of Certain State Dependent Branching Processes.
Abstract
Let (X sub n) denote the Galton-Watson branching process with the following modifications: Whenever (X sub n) = 0, X sub(n + 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 k(i) 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 k(i), zeta(i) are presented which are sufficient for transience, recurrence, and positive-recurrence of (X sub n).
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1974
- Accession Number
- ADA001660
Entities
People
- William M. Stein
Organizations
- University of Wisconsin–Madison