Deterministic approximation of a sequence of nearly critical branching processes

I. Rahimov

doi:10.1080/07362990802286442

Deterministic approximation of a sequence of nearly critical branching processes

I. Rahimov^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

13 Scopus citations

Abstract

We consider a sequence of discrete time nearly critical branching processes with time-dependent immigration. Using a martingale approach, we prove that when the immigration mean tends to infinity depending on the time of immigration, the suitable normalized sequence can be approximated in Skorokhod metric by a deterministic process. Consequences related to the maxima and the total progeny of the process will be discussed.

Original language	English
Pages (from-to)	1013-1024
Number of pages	12
Journal	Stochastic Analysis and Applications
Volume	26
Issue number	5
DOIs	https://doi.org/10.1080/07362990802286442
State	Published - Sep 2008

Bibliographical note

Funding Information:
Received November 11, 2007; Accepted February 22, 2008. This article is based on a part of results obtained under research project No. IN080396 funded by KFUPM, Dhahran, Saudi Arabia. My sincere thanks to King Fahd University of Petroleum and Minerals for support and facilities. Address correspondence to I. Rahimov, Department of Mathematics and Statistics, KFUPM, Box 1339, Dhahran 31261, Saudi Arabia; E-mail: rahimov@ kfupm. edu.sa

Keywords

Branching process
Maxima
Skorokhod space
Time-dependent immigration
Total progeny

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1080/07362990802286442

Cite this

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abstract = "We consider a sequence of discrete time nearly critical branching processes with time-dependent immigration. Using a martingale approach, we prove that when the immigration mean tends to infinity depending on the time of immigration, the suitable normalized sequence can be approximated in Skorokhod metric by a deterministic process. Consequences related to the maxima and the total progeny of the process will be discussed.",

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N1 - Funding Information: Received November 11, 2007; Accepted February 22, 2008. This article is based on a part of results obtained under research project No. IN080396 funded by KFUPM, Dhahran, Saudi Arabia. My sincere thanks to King Fahd University of Petroleum and Minerals for support and facilities. Address correspondence to I. Rahimov, Department of Mathematics and Statistics, KFUPM, Box 1339, Dhahran 31261, Saudi Arabia; E-mail: rahimov@ kfupm. edu.sa

PY - 2008/9

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N2 - We consider a sequence of discrete time nearly critical branching processes with time-dependent immigration. Using a martingale approach, we prove that when the immigration mean tends to infinity depending on the time of immigration, the suitable normalized sequence can be approximated in Skorokhod metric by a deterministic process. Consequences related to the maxima and the total progeny of the process will be discussed.

AB - We consider a sequence of discrete time nearly critical branching processes with time-dependent immigration. Using a martingale approach, we prove that when the immigration mean tends to infinity depending on the time of immigration, the suitable normalized sequence can be approximated in Skorokhod metric by a deterministic process. Consequences related to the maxima and the total progeny of the process will be discussed.

KW - Branching process

KW - Maxima

KW - Skorokhod space

KW - Time-dependent immigration

KW - Total progeny

UR - https://www.scopus.com/pages/publications/50949090495

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DO - 10.1080/07362990802286442

M3 - Article

AN - SCOPUS:50949090495

SN - 0736-2994

VL - 26

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JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

IS - 5

ER -

Deterministic approximation of a sequence of nearly critical branching processes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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