# 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.

## 16 Citations

### Subcritical Branching Processes in Random Environment with Immigration Stopped at Zero

- MathematicsJournal of Theoretical Probability
- 2020

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

- MathematicsJournal of Theoretical Probability
- 2020

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…

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

- MathematicsStochastics and Quality Control
- 2021

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

- MathematicsActa Mathematica Scientia
- 2021

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

- MathematicsMathematics
- 2021

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

- MathematicsActa Mathematica Scientia
- 2021

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

- Mathematics
- 2022

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

- Mathematics
- 2021

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

- Mathematics
- 2022

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…

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The Galton-Watson process with immigration which is time-homogeneous but not permitted when the process is in state 0 (so that this state is absorbing) is briefly studied in the subcritical and…

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We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The…

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For a branching process in random environment, it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other.…

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On donne des conditions suffisantes d'existence d'une distribution limite pour un processus ramifie multitype avec immigration dans un environnement aleatoire

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© Foundation Compositio Mathematica, 1975, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions…