Weakly supercritical branching process in unfavourable environment
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Valeriy I. Afanasyev
Abstract
Let {Zn} be a weakly supercritical branching process in a random environment, and {Sn} be its associated random walk. We consider a natural martingale Wn = Znexp(−Sn), where n ≥ 0. We prove two limit theorems for the random process W⌊nt⌋, where t ∈ [0, 1], which is considered either under the condition on the unfavourable environment {max1≤i≤nSi} or under the condition on the unfavourable environment {Sn ≤ u}, where u is some positive constant.
Originally published in Diskretnaya Matematika (2022) 34, №3, 3–19 (in Russian).
Funding statement: This work was supported by the Russian Science Foundation under grant №19-11-00111, https://rscf.ru/project/19-11-00111/.
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Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
