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Measure change in multitype branching. (English) Zbl 1056.60082
There exists in branching a connection between stochastic dominance of the offspring distribution, moment conditions, and mean convergence of certain martingales. This phenomenon is studied here in a fairly general framework, extending the approach of R. Lyons, R. Permantle, and Y. Peres [Ann. Probab. 23, 1125–1138 (1995; Zbl 0840.60077)]. The results are applied to various branching models, in particular, branching random walks, in order to obtain convergence results not readily accessible using classical methods.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G42 Martingales with discrete parameter
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