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Genealogical constructions and asymptotics for continuous-time Markov and continuous-state branching processes
Ist Teil von
Advances in applied probability, 2018-12, Vol.50 (A), p.197-209
Ort / Verlag
Cambridge, UK: Cambridge University Press
Erscheinungsjahr
2018
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Genealogical constructions of population processes provide models which simultaneously record the forward-in-time evolution of the population size (and distribution of locations and types for models that include them) and the backward-in-time genealogies of the individuals in the population at each time t. A genealogical construction for continuous-time Markov branching processes from Kurtz and Rodrigues (2011) is described and exploited to give the normalized limit in the supercritical case. A Seneta‒Heyde norming is identified as a solution of an ordinary differential equation. The analogous results are given for continuous-state branching processes, including proofs of the normalized limits of Grey (1974) in both the supercritical and critical/subcritical cases.