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A class of subcritical branching processes with immigration and infinite number of types of particles
Published/Copyright:
May 16, 2007
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 Ti 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 Ti turns into a set of particles of types Ti and Ti + 1. It is proved that the probability distributions of the vectors
(r, t ) converge as t → ∞ to discrete limit distributions.
Published Online: 2007-05-16
Published in Print: 2007-04-19
Copyright 2007, Walter de Gruyter
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Articles in the same Issue
- A class of subcritical branching processes with immigration and infinite number of types of particles
- Bounds for extremal values of the mean number of cells containing a given number of particles
- Limit theorems for the number of solutions of a system of random linear equations belonging to a given set
- On the Stein–Tikhomirov method and its applications in nonclassical limit theorems
- Shifted products of independent random variables with values in finite groups
- Optimal management of two parallel stacks in two-level memory
- An upper bound for the number of product-free sets in a class of groups
- Mark sequences in multigraphs
- Classes of lexicographic equivalence in Euclidean combinatorial optimisation on arrangements
- Representations over Galois ring of a linear recurring sequence of maximal period over Galois field
