Asymptotic behavior of a controlled branching process with continuous state space

I. Rahimov

doi:10.1080/07362990601139545

Asymptotic behavior of a controlled branching process with continuous state space

I. Rahimov^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this article, a modification of the branching stochastic process with immigration and with continuous states, introduced by Adke and Gadag [1] will be considered. Theorems establishing a relationship of this process with Bienaymé-Galton-Watson processes will be proved. It will be demonstrated that limit theorems for the new process can be deduced from those for simple processes with time-dependent immigration, assuming that process is critical and offspring variance is finite.

Original language	English
Pages (from-to)	337-352
Number of pages	16
Journal	Stochastic Analysis and Applications
Volume	25
Issue number	2
DOIs	https://doi.org/10.1080/07362990601139545
State	Published - Mar 2007

Bibliographical note

Funding Information:
Accepted September 29, 2006 This article is based on results of research project No FT-2005/01 funded by KFUPM, Dhahran, Saudi Arabia. The author is indebted to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for excellent research facilities. He also thanks the referee for careful reading of the first version of the paper and for valuable comments.

Keywords

Branching process
Counting process
Immigration
Independent increment

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/07362990601139545

Cite this

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title = "Asymptotic behavior of a controlled branching process with continuous state space",

abstract = "In this article, a modification of the branching stochastic process with immigration and with continuous states, introduced by Adke and Gadag [1] will be considered. Theorems establishing a relationship of this process with Bienaym{\'e}-Galton-Watson processes will be proved. It will be demonstrated that limit theorems for the new process can be deduced from those for simple processes with time-dependent immigration, assuming that process is critical and offspring variance is finite.",

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author = "I. Rahimov",

note = "Funding Information: Accepted September 29, 2006 This article is based on results of research project No FT-2005/01 funded by KFUPM, Dhahran, Saudi Arabia. The author is indebted to King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, for excellent research facilities. He also thanks the referee for careful reading of the first version of the paper and for valuable comments.",

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N2 - In this article, a modification of the branching stochastic process with immigration and with continuous states, introduced by Adke and Gadag [1] will be considered. Theorems establishing a relationship of this process with Bienaymé-Galton-Watson processes will be proved. It will be demonstrated that limit theorems for the new process can be deduced from those for simple processes with time-dependent immigration, assuming that process is critical and offspring variance is finite.

AB - In this article, a modification of the branching stochastic process with immigration and with continuous states, introduced by Adke and Gadag [1] will be considered. Theorems establishing a relationship of this process with Bienaymé-Galton-Watson processes will be proved. It will be demonstrated that limit theorems for the new process can be deduced from those for simple processes with time-dependent immigration, assuming that process is critical and offspring variance is finite.

KW - Branching process

KW - Counting process

KW - Immigration

KW - Independent increment

UR - https://www.scopus.com/pages/publications/33947173190

U2 - 10.1080/07362990601139545

DO - 10.1080/07362990601139545

M3 - Article

AN - SCOPUS:33947173190

SN - 0736-2994

VL - 25

SP - 337

EP - 352

JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 2

ER -

Asymptotic behavior of a controlled branching process with continuous state space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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