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B. A. Sevastyanov

A class of subcritical branching processes with immigration and infinite number of types of particles

We consider a subcritical branching process with immigration, infinite number of types T₁, T₂, ... of particles, and discrete time. The state of the process at the moment of time t is the set of vectors

where ξi (t) is the number of particles of type T_i at the moment of time t, i = 1, 2, ... It is assumed that at each moment of time only particles of type T₁ immigrate and each particle of type T_i turns into a set of particles of types T_i and T_{i + 1}. It is proved that the probability distributions of the vectors (r, t ) converge as t → ∞ to discrete limit distributions.

Discrete Mathematics and Applications, Walter de Gruyter

Print ISSN: 0924-9266
Volume: 17, 04/2007
Pages: 1 - 5

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