Limit Theorems for the Simple Branching Process Allowing Immigration. II. The Case of Infinite Offspring Mean.
Abstract
This paper obtains some limit theorems for the simple branching process allowing immigra-X sub n) when the offspring mean is infinite. It is shown that there exists a function U such that (e to the -nth power) converges almost surely and if s = Sum over b sub j log(+) U(j) < infinity, where (b sub j) is the immigration distribution, the limit is non-defective and non-degenerate but is infinite if s = infinity. When s = infinity limit theorems are found for (U(X sub n)) which involve a slowly varying non-linear norming. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1977
- Accession Number
- ADA049693
Entities
People
- A. D. Barbour
- Anthony G. Pakes
Organizations
- Princeton University