Abstract
A continuous-time Markov branching process with a single type T of particles is considered in which any pair of particles T+T produces offspring independently of all other particles. In addition, any particle of type T also produces children. Representations for the extinction probabilities of this process are obtained under certain assumptions on the offspring distribution. To establish this result we apply the exponential generating function method for the solution of a stationary backward Kolmogorov system of differential equations (see [A. V. Kalinkin, {Theory Probab. Appl., 27 (1982), pp.~201--205]).
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