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 journalArticlepeer-review

16 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 languageEnglish
Pages (from-to)122-143
Number of pages22
JournalJournal of Theoretical Probability
Volume25
Issue number1
DOIs
Publication statusPublished - Mar 2012
Externally publishedYes

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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