Additional aspects of the generalized linear-fractional branching processReport as inadecuate

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* Corresponding author 1 LPTM - Laboratoire de Physique Théorique et Modélisation

Abstract : We derive some additional results on the Bienyamé-Galton-Watson branching process with θ−linear fractional branching mechanism, as studied in 16. This includes: the explicit expression of the limit laws in both the sub-critical cases and the super-critical cases with finite mean, the long-run behavior of the population size in the critical case, limit laws in the super-critical cases with infinite mean when the θ-process is either regular or explosive, results regarding the time to absorption, an expression of the probability law of the θ-branching mechanism involving Bell polynomials, the explicit computation of the stochas-tic transition matrix of the θ−process, together with its powers.

Keywords : Bienyamé-Galton-Watson branching process Yaglom limits powers of probability transition matrix θ−linear fractional branching mechanism population growth

Author: Nicolas Grosjean - Thierry Huillet -



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