On the extinction times of varying and random environment branching processes
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In this paper, the extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.Abstract:
Bounds are derived for the probability of extinction by the nth generation for a branching process in a varying environment. From these bounds, necessary and sufficient conditions are established for such a process to become extinct with probability one. The extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.read more
Citations
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Criticality for branching processes in random environment
TL;DR: In this article, the authors studied branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type and the main properties of such branching processes are developed under a general assumption, known as Spitzer's condition in fluctuation theory of random walks, and some additional moment condition.
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Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
TL;DR: In this article, the authors considered weakly subcritical and supercritical conditional random walks and proved functional limit theorems for conditional supercriticality and weak subcriticality, respectively.
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Conditional limit theorems for intermediately subcritical branching processes in random environment
TL;DR: In this article, the authors consider a processus de branchement dans un environnement aleatoire, where the distribution des enfants des individus varie aleatoirement de facon independante d’une generation a l’autre.
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On the survival probability of a branching process in a finite state i.i.d. environment
TL;DR: In this article, the authors determine the asymptotic behavior of the survival probability of a branching process in a finite state i.i.d. random environment, and show that the probability of such a process is bounded.
References
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Journal ArticleDOI
Branching Processes with Random Environments, II: Limit Theorems
Krishna B. Athreya,Samuel Karlin +1 more
Journal ArticleDOI
Galton-watson processes in varying environments
TL;DR: Galton-Watson processes where reproduction of individuals in different generations can have different distributions retain many characteristic features of classical processes as mentioned in this paper, and they have been shown to retain many of the characteristics of classical Galton Watson processes.
Journal ArticleDOI
Survival of Mutant Genes
TL;DR: A possible transition from the strongly stochastic stage to the mainly deterministic stage of the evolution of a mutation is discussed in an attempt to connect the present work with the evolutionary dynamics of large populations.
Journal ArticleDOI
Bounds on the extinction time distributions of some branching processes
TL;DR: The class of fractional linear generating functions, one of the few known classes of probability generating functions whose iterates can be explicitly stated, is examined in this article, where the best possible bounds for the expected time to extinction of the corresponding Poisson branching process are obtained.
Journal ArticleDOI
Some effects of fluctuating offspring distributions on the survival of a gene
TL;DR: In this paper, the fate of a new gene introduced into a large population that is stationary in size is studied, where lines descended from two or more genes of this type develop independently of each other.
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