Markov limit of line of decent types in a multitype supercritical branching process

Jyy-I Hong and K.B. Athreya

Statistics & Probability Letters, 2015, vol. 98, issue C, 54-58

Abstract: In a multitype (d types) supercritical positively regular Galton–Watson branching process, let {Xn,Xn−1,…,X0} denote the types of a randomly chosen (i.e., uniform distribution) individual from the nth generation and this individual’s n ancestors. It is shown here that this sequence converges in distribution to a Markov chain {Y0,Y1,…} with transition probability matrix (pij)1≤i,j≤d and having the stationary distribution. We also consider the critical case conditioned on non-extinction.

Keywords: Branching processes; Multitype; Supercritical; Markov (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715214003824
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:98:y:2015:i:c:p:54-58

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2014.11.013

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().