Large deviations of bisexual branching process in random environment
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Aleksandr V. Shklyaev
Abstract
We study large deviation probabilities for bisexual branching process in a random (i.i.d.) environment. Under several conditions on the mating function (which may depend on the environment) we introduce the associated random walk of the process. We also assume Cramer condition for the step of the walk and moment conditions on the number of descendants of one pair. Under Cramer condition for the steps of the walk and moment conditions on the number of descendants of a pair we find an exact asymptotics of probabilities P(ln Nn ∈ [x, x + Δn)) as n → ∞ for x/n varying in some domain for all sequences Δn, tending to zero sufficiently slowly. Similar results we obtain for bisexual branching process with immigration in a random environment.
Originally published in Diskretnaya Matematika (2023) 35, №3, 125–142 (in Russian).
Funding statement: The work was supported by the Russian Science Foundation under grant no. 19-11-00111-P, https://rscf.ru/project/19-11-00111/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences.
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the number of particles from a marked set of cells for an analogue of a general allocation scheme
- Scaling of graphs with diameter constraint
- On the maximal tree in Galton–Watson forest with infinite variance of the offspring
- Short tests for contact circuits with similar-type weakly connected faults of contacts
- Large deviations of bisexual branching process in random environment
- Properties of critical branching random walks on the line under non-extinction condition
Artikel in diesem Heft
- Frontmatter
- On the number of particles from a marked set of cells for an analogue of a general allocation scheme
- Scaling of graphs with diameter constraint
- On the maximal tree in Galton–Watson forest with infinite variance of the offspring
- Short tests for contact circuits with similar-type weakly connected faults of contacts
- Large deviations of bisexual branching process in random environment
- Properties of critical branching random walks on the line under non-extinction condition
