Reduced critical Bellman–Harris branching processes for small populations
-
Vladimir A. Vatutin
,
Wenming Hong
Abstract
A critical Bellman-Harris branching process {Z(t),t ≥ 0} with finite variance of the offspring number is considered. Assuming that 0 < Z(t) ≤ φ(t), where either φ(t) = o(t) as t → ∞ or φ(t) = at,a>0, we study the structure of the process where Z(s,t) is the number of particles in the initial process at moment s which either survive up to moment t or have a positive number of descendants at this moment.
Originally published in Diskretnaya Matematika (2018) 30,No 3, 25–39 (in Russian).
Funding
The work of V.A. Vatutin was supported by the Russian Science Foundation under grant no. 14-50-00005, the work of Wenming Hong and Yao Ji was supported by Natural Science Foundation of China under grants 11531001 and 11626245.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
Artikel in diesem Heft
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
