Branching processes in a random environment with immigration stopped at zero

@article{Dyakonova2019BranchingPI,
  title={Branching processes in a random environment with immigration stopped at zero},
  author={Elena Dyakonova and Doudou Li and Vladimir Vatutin and Mei Zhang},
  journal={Journal of Applied Probability},
  year={2019},
  volume={57},
  pages={237 - 249}
}
Abstract A critical branching process with immigration which evolves in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the population, we investigate the tail distribution of the so-called life period of the process, i.e. the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. 
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16 Citations
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16 Citations

Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero

We consider the subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as…

Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero

We consider the subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as…

A critical branching process with immigration in random environment

Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment

Abstract We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be…

Moments and large deviations for supercritical branching processes with immigration in random environments

Let ( Z n ) be a branching process with immigration in a random environment ξ , where ξ is an independent and identically distributed sequence of random variables. We show asymptotic properties for…

Period-Life of a Branching Process with Migration and Continuous Time

The boundary theorem for theperiod-life of the subcritical or critical branching process with migration was found and the probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained.

Moments and large deviations for supercritical branching processes with immigration in random environments

Let (Zn) be a branching process with immigration in a random environment ξ, where ξ is an independent and identically distributed sequence of random variables. We show asymptotic properties for all…

Exact convergence rate in the central limit theorem for a branching process with immigration in a random environment

Let ( Z n ) be a branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the…

Limit theorems for the critical Galton-Watson processes with immigration stopped at zero

In this paper, we consider a critical Galton-Watson branching process with immigration stopped at zero W. Some precise estimation on the generation function of the n-th population are obtained, and…

Central limit theorem and Berry-Esseen bounds for a branching random walk with immigration in a random environment

We consider a branching random walk on d -dimensional real space with immigration in a time-dependent random environment. Let Z n ( t ) be the so-called partition function of the process, namely, the…

22 References

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