N. O’Connell, “Yule Process Approximation of the Skeleton of a Branching Process,” Journal of Applied Probability, Vol. 30, No. 3, 1993, pp. 725-729. doi:10.2307/3214778

has been cited by the following article:

• TITLE: Decomposition of Supercritical Linear-Fractional Branching Processes

  AUTHORS: Serik Sagitov, Altynay Shaimerdenova

  KEYWORDS: Harris-Sevastyanov Transformation; Dual Reproduction Law; Branching Process with Countably Many Types; Multivariate Linear-Fractional Distribution; Bienaymé-Galton-Watson Process; Conditioned Branching Process

  JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 27, 2013

  ABSTRACT: 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.