Limit theorems for the simple branching process allowing immigration, II. The case of infinite offspring mean
- 1 March 1979
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 11 (1) , 63-72
- https://doi.org/10.2307/1426768
Abstract
This paper presents some limit theorems for the simple branching process allowing immigration, {Xn}, when the offspring mean is infinite. It is shown that there exists a function U such that {e–nU/(Xn)} converges almost surely, and if s = ∑ bj, log+U(j) < ∞, where {bj} is the immigration distribution, the limit is non-defective and non-degenerate but is infinite if s = ∞.When s = ∞, limit theorems are found for {U(Xn)} which involve a slowly varying non-linear norming.Keywords
This publication has 3 references indexed in Scilit:
- Limit theorems for the simple branching process allowing immigration, I. The case of finite offspring meanAdvances in Applied Probability, 1979
- A note on simple branching processes with infinite meanJournal of Applied Probability, 1977
- On the asymptotic behaviour of branching processes with infinite meanAdvances in Applied Probability, 1977