Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 37, Number 2 (2005), 523-538.
Fluctuation limit of branching processes with immigration and estimation of the means
We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n3/2, in contrast to both the subcritical case, in which it is n1/2, and the nearly critical case with positive limiting offspring variance, in which it is n.
Adv. in Appl. Probab. Volume 37, Number 2 (2005), 523-538.
First available in Project Euclid: 15 June 2005
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62F12: Asymptotic properties of estimators
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J60: Diffusion processes [See also 58J65] 62M05: Markov processes: estimation
Ispány, M.; Pap, G.; van Zuijlen, M. C. A. Fluctuation limit of branching processes with immigration and estimation of the means. Adv. in Appl. Probab. 37 (2005), no. 2, 523--538. doi:10.1239/aap/1118858637. http://projecteuclid.org/euclid.aap/1118858637.