Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment-Reference-Cited by-同舟云学术

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

Published:2021-11-17 Issue:2 Volume:36 Page:129-143
ISSN:2367-2390
Container-title:Stochastics and Quality Control
language:en
Short-container-title:

Author:

Afanasyev Valeriy Ivanovich¹

Affiliation:

1. Steklov Mathematical Institute of Russian Academy of Sciences , 8 Gubkin St. , Moscow , 119991 , Russia

Abstract

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 geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till + ∞

+\infty

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Safety, Risk, Reliability and Quality,Statistics and Probability

Link

https://www.degruyter.com/document/doi/10.1515/eqc-2021-0036/pdf

Reference11 articles.

1. V. I. Afanasyev, About time of reaching a high level by a random walk in a random environment, Theory Probab. Appl. 57 (2013), no. 4, 547–567.

2. V. I. Afanasyev, On the time of attaining a high level by a transient random walk in a random environment, Theory Probab. Appl. 61 (2017), no. 2, 178–207.

3. V. I. Afanasyev, On the non-recurrent random walk in a random environment, Discrete Math. Appl. 28 (2018), no. 3, 139–156.

4. V. I. Afanasyev, A critical branching process with immigration in random environment, Stochastic Process. Appl. 139 (2021), 110–138.

5. K. B. Athreya and P. E. Ney, Branching Processes, Grundlehren Math. Wiss. 196, Springer, New York, 1972.

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