Advances in Applied Probability

Fluctuation limit of branching processes with immigration and estimation of the means

M. Ispány, G. Pap, and M. C. A. van Zuijlen

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
Adv. in Appl. Probab. Volume 37, Number 2 (2005), 523-538.

Dates
First available in Project Euclid: 15 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.aap/1118858637

Digital Object Identifier
doi:10.1239/aap/1118858637

Mathematical Reviews number (MathSciNet)
MR2144565

Zentralblatt MATH identifier
1069.62065

Subjects
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

Keywords
Conditional least-squares estimator fluctuation limit nearly critical Galton-Watson branching process with immigration Ornstein-Uhlenbeck-type process

Citation

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.


Export citation