Asymptotic Properties of the Markov Branching Process with Immigration

Junping Li; Anyue Chen; Anthony G. Pakes

doi:10.1007/s10959-010-0301-z

Asymptotic Properties of the Markov Branching Process with Immigration

Junping Li, Anyue Chen^*, Anthony G. Pakes

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.

Original language	English
Pages (from-to)	122-143
Number of pages	22
Journal	Journal of Theoretical Probability
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s10959-010-0301-z
Publication status	Published - Mar 2012
Externally published	Yes

Keywords

λ-invariant measure and function
Conditional limit theorem
Construction and uniqueness
Decay parameter
Immigration
Markov branching process
Nonconservative q-matrix

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10.1007/s10959-010-0301-z

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abstract = "We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.",

keywords = "λ-invariant measure and function, Conditional limit theorem, Construction and uniqueness, Decay parameter, Immigration, Markov branching process, Nonconservative q-matrix",

author = "Junping Li and Anyue Chen and Pakes, {Anthony G.}",

note = "Funding Information: Acknowledgements The authors would like to express their sincere thanks for the anonymous referees in providing vert helpful comments and suggestions. The work described in this paper by Chen Anyue and Li Junping was substantially supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, PRC, Project HKU 7010/06P, and the National Natural Sciences Foundation of China (No.10771216), respectively.",

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AU - Chen, Anyue

AU - Pakes, Anthony G.

N1 - Funding Information: Acknowledgements The authors would like to express their sincere thanks for the anonymous referees in providing vert helpful comments and suggestions. The work described in this paper by Chen Anyue and Li Junping was substantially supported by the grants from the Research Grants Council of the Hong Kong Special Administrative Region, PRC, Project HKU 7010/06P, and the National Natural Sciences Foundation of China (No.10771216), respectively.

PY - 2012/3

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N2 - We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.

AB - We consider the Markov branching process with immigration allowing the possibility of infinite numbers of offspring and/or immigrants. Our focus is on the construction and uniqueness of the minimal transition function and on its asymptotic behavior. Conditional limit theorems for the population size are given in cases for which the transition function is dishonest.

KW - λ-invariant measure and function

KW - Conditional limit theorem

KW - Construction and uniqueness

KW - Decay parameter

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KW - Markov branching process

KW - Nonconservative q-matrix

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JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

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Asymptotic Properties of the Markov Branching Process with Immigration

Abstract

Keywords

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