Computation of Final Probabilities for Branching Random Processes

Abstract

The terminology and notation in this paper are close to those in [1]. In what follows, we consider discrete schemes homogeneous in time t:t runs only through 1, 2, 3,… and can be interpreted as the “generation number” of the particle in question. Accordingly, is the probability that one particle of type T _k gives α₁, α₂,…, α _n particles of the types T ₁, T ₂,…, T _n , respectively in t generations. All further computations are based on the generating functions of the probabilities of the various transitions during one generation. Using these probabilities, we define by induction the generating functions for all positive integers t:

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Dokl. Akad. Nauk SSSR56:8 (1947), 783-786.