Multitype branching limit behavior
The authors define a multitype (\(p\)-type) branching process in a varying environment. In the varying environment settings, the natural object of the study appears to be linear combinations of the type sizes of successive generations. A certain sequence of such linear combination possesses some convergence properties. This sequence turns out to be instrumental in deriving a condition for continuity of the limiting distribution function. For related papers see: \textit{J. D. Biggins}, \textit{H. Cohn} and \textit{O. Nerman} [Stochastic Processes Appl. 83, 357-400 (1999; Zbl 0997.60093)]; \textit{T. Hattori} [J. Math. Sci., Tokyo 4, 229-278 (1997; Zbl 0895.60085)] and \textit{O. D. Jones} [Ann. Appl. Probab. 7, 772-801 (1997; Zbl 0885.60077)].
scientific article; zbMATH DE number 2005164