Additional aspects of the generalized linear-fractional branching process

Abstract

We derive some additional results on the Bienyamé-Galton-Watson branching process with $\theta -$linear fractional branching mechanism, as studied in \cite{Sag}. 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 $\theta$-process is either regular or explosive, results regarding the time to absorption, an expression of the probability law of the $\theta$-branching mechanism involving Bell polynomials, the explicit computation of the stochastic transition matrix of the $\theta -$process, together with its powers.

arXiv commentTo appear in Annals of the Institute of Statistical Mathematics

References in corpus (1)

• The fixation line in the $\Lambda$-coalescent

Cited by in corpus (1)

• Some Combinatorial Aspects of Discrete Non-linear Population Dynamics