Hong, Jyy-I ; Athreya, K.B. (2015) Markov limit of line of decent types in a multitype supercritical branching process Statistics & Probability Letters, 98 . pp. 54-58. ISSN 01677152
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Official URL: http://doi.org/10.1016/j.spl.2014.11.013
Related URL: http://dx.doi.org/10.1016/j.spl.2014.11.013
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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier B.V. |
| Keywords: | Branching processes, Multitype, Supercritical, Markov |
| ID Code: | 131571 |
| Deposited On: | 07 Dec 2022 07:25 |
| Last Modified: | 07 Dec 2022 07:25 |
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