Limiting behavior of a generalized branching process with immigration

I. Rahimov; W. S. Al-Sabah

doi:10.1016/j.spl.2007.05.027

Limiting behavior of a generalized branching process with immigration

I. Rahimov^*
, W. S. Al-Sabah

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

1 Scopus citations

Abstract

In the paper a modification of the branching process with continuous states, introduced by Adke and Gadag [1995. A new class of branching processes. Branching Processes. In: Proceedings of the First World Congress, Lecture Notes in Statistics, Springer, Berlin, vol. 99, pp. 90-105] is considered. Theorems establishing connection between asymptotic behavior of this process and the Bienaymé-Galton-Watson process are proved. Applications in the case of the process without and with stationary immigration are provided.

Original language	English
Pages (from-to)	225-230
Number of pages	6
Journal	Statistics and Probability Letters
Volume	78
Issue number	3
DOIs	https://doi.org/10.1016/j.spl.2007.05.027
State	Published - 15 Feb 2008

Bibliographical note

Funding Information:
The results in this article are part of project No. FT-2005/01 funded by King Fahd University of Petroleum and Minerals. We are grateful to the referee for the careful reading of the first version of the paper and for his valuable comments.

Keywords

Branching process
Counting process
Immigration
Independent increment
Stationary

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2007.05.027

Cite this

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title = "Limiting behavior of a generalized branching process with immigration",

abstract = "In the paper a modification of the branching process with continuous states, introduced by Adke and Gadag [1995. A new class of branching processes. Branching Processes. In: Proceedings of the First World Congress, Lecture Notes in Statistics, Springer, Berlin, vol. 99, pp. 90-105] is considered. Theorems establishing connection between asymptotic behavior of this process and the Bienaym{\'e}-Galton-Watson process are proved. Applications in the case of the process without and with stationary immigration are provided.",

keywords = "Branching process, Counting process, Immigration, Independent increment, Stationary",

author = "I. Rahimov and Al-Sabah, \{W. S.\}",

note = "Funding Information: The results in this article are part of project No. FT-2005/01 funded by King Fahd University of Petroleum and Minerals. We are grateful to the referee for the careful reading of the first version of the paper and for his valuable comments.",

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AU - Al-Sabah, W. S.

N1 - Funding Information: The results in this article are part of project No. FT-2005/01 funded by King Fahd University of Petroleum and Minerals. We are grateful to the referee for the careful reading of the first version of the paper and for his valuable comments.

PY - 2008/2/15

Y1 - 2008/2/15

N2 - In the paper a modification of the branching process with continuous states, introduced by Adke and Gadag [1995. A new class of branching processes. Branching Processes. In: Proceedings of the First World Congress, Lecture Notes in Statistics, Springer, Berlin, vol. 99, pp. 90-105] is considered. Theorems establishing connection between asymptotic behavior of this process and the Bienaymé-Galton-Watson process are proved. Applications in the case of the process without and with stationary immigration are provided.

AB - In the paper a modification of the branching process with continuous states, introduced by Adke and Gadag [1995. A new class of branching processes. Branching Processes. In: Proceedings of the First World Congress, Lecture Notes in Statistics, Springer, Berlin, vol. 99, pp. 90-105] is considered. Theorems establishing connection between asymptotic behavior of this process and the Bienaymé-Galton-Watson process are proved. Applications in the case of the process without and with stationary immigration are provided.

KW - Branching process

KW - Counting process

KW - Immigration

KW - Independent increment

KW - Stationary

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DO - 10.1016/j.spl.2007.05.027

M3 - Article

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SN - 0167-7152

VL - 78

SP - 225

EP - 230

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

Limiting behavior of a generalized branching process with immigration

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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