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Uniqueness and extinction properties of generalised Markov branching processes. (English) Zbl 1010.60076
If in a continuous-time Galton-Watson process branching of a particle occurs with rate r>0, and the system is in the state i, then the next branching event occurs with rate ir. R.-R. Chen [J. Appl. Probab. 34, No. 1, 14-23 (1997; Zbl 0874.60078)] discussed a generalization of this classical model by assuming that for a fixed number ν>0 the next branching event occurs with rate i ν r instead, for all i0. In the present paper it is shown that this leads to a unique process. Extinction properties are also studied.

MSC:
60J80Branching processes