Document Zbl 1358.60060

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Criterion for unlimited growth of critical multidimensional stochastic models. (English) Zbl 1358.60060

Adv. Appl. Probab. 48, No. 4, 972-988 (2016).

Summary: We give a criterion for unlimited growth with positive probability for a large class of multidimensional stochastic models. As a by-product, we recover the necessary and sufficient conditions for recurrence and transience for critical multitype Galton-Watson with immigration processes and also significantly improve some results on multitype size-dependent Galton-Watson processes.

Cited in 1 Document

MSC:

60G42	Martingales with discrete parameter
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J10	Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

stochastic difference equation; Lyapunov function; martingale; Galton-Watson processes

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