Properties of multitype subcritical branching processes in random environment
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Vladimir A. Vatutin
and
Elena E. Dyakonova
Abstract
We study properties of a p-type subcritical branching process in random environment initiated at moment zero by a vector z = (z1, .., zp) of particles of different types. For p = 1 the class of processes we consider corresponds to the so-called strongly subcritical case. It is shown that the survival probability of this process up to moment n behaves as C(z)λn for large n, where the parameters λ ∈ (0, 1) and C(z) ∈ (0, ∞) are explicitly described in terms of the characteristics of the process. We also demonstrate that the distribution of the number of particles of different types at moment n → ∞ (given its survival up to this moment) does not asymptotically depend on the number and types of particles initiated the process.
Originally published in Diskretnaya Matematika (2020) 32,№3, 3–23 (in Russian).
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Funding: This work was supported by the Russian Science Foundation under the grant 17-11-01173.
References
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Articles in the same Issue
- Frontmatter
- Diagnostic tests under shifts with fixed filling tuple
- On the average-case complexity of Boolean functions under binomial distribution on their domains
- Boolean analogues of the Pascal triangle with maximal possible number of ones
- The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups
- On the complexity of monotone circuits for threshold symmetric Boolean functions
- Properties of multitype subcritical branching processes in random environment
Articles in the same Issue
- Frontmatter
- Diagnostic tests under shifts with fixed filling tuple
- On the average-case complexity of Boolean functions under binomial distribution on their domains
- Boolean analogues of the Pascal triangle with maximal possible number of ones
- The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups
- On the complexity of monotone circuits for threshold symmetric Boolean functions
- Properties of multitype subcritical branching processes in random environment
