The survival probability of a critical multitype Galton-Watson branching process
The classical Kolmogorov theorem on the rate of decay of the probability of non-extinction in a critical branching process was recently given a probabilistic proof, sometimes also known nowadays as a conceptual proof, by \textit{J. Geiger} [J. Appl. Probab. 36, No. 2, 301-309 (1999; Zbl 0942.60071)]. This proof involves a particular decomposition of the Galton-Watson tree conditioned on survival up to a given generation. The present paper provides an analogous proof of the corresponding result for the critical multitype Galton-Watson branching process in which all family size distributions have finite variances.
scientific article; zbMATH DE number 1756317