Journal of Applied Probability

Coalescence on critical and subcritical multitype branching processes

Jyy-I Hong

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

Consider a d-type (d<∞) Galton–Watson branching process, conditioned on the event that there are at least k≥2 individuals in the nth generation, pick k individuals at random from the nth generation and trace their lines of descent backward in time till they meet. In this paper, the limit behaviors of the distributions of the generation number of the most recent common ancestor of any k chosen individuals and of the whole population are studied for both critical and subcritical cases. Also, we investigate the limit distribution of the joint distribution of the generation number and their types.

Article information

Source
J. Appl. Probab., Volume 53, Number 3 (2016), 802-817.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1476370777

Mathematical Reviews number (MathSciNet)
MR3570095

Zentralblatt MATH identifier
1351.60113

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations

Keywords
Branching process coalescence critical subcritical multitype line of descent

Citation

Hong, Jyy-I. Coalescence on critical and subcritical multitype branching processes. J. Appl. Probab. 53 (2016), no. 3, 802--817. https://projecteuclid.org/euclid.jap/1476370777


Export citation

References

  • Athreya, K. B. (2012). Coalescence in critical and subcritical Galton–Watson branching processes. J. Appl. Prob. 49, 627–638.
  • Athreya, K. B. (2012). Coalescence in the recent past in rapidly growing populations. Stoch. Process. Appl. 122, 3757–3766.
  • Athreya, K. B. and Ney, P. E. (2004). Branching Processes. Dover, Mineola, NY.
  • Hong, J. (2013). Coalescence in subcritical Bellman–Harris age-dependent branching processes. J. Appl. Prob. 50, 576–591.
  • Hong, J. (2015). Coalescence on supercritical multi-type branching processes. Sankhyā A 77, 65–78.
  • Joffe, A. and Spitzer, F. (1967). On multitype branching processes with $\rho\leq 1$. J. Math. Anal. Appl. 19, 409–430.
  • Kallenberg, O. (1986). Random Measures, 4th edn. Akademie-Verlag, Berlin.