Decomposition of Supercritical Linear-Fractional Branching Processes


It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.

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S. Sagitov and A. Shaimerdenova, "Decomposition of Supercritical Linear-Fractional Branching Processes," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 352-359. doi: 10.4236/am.2013.42054.

Conflicts of Interest

The authors declare no conflicts of interest.


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