Poisson random measures and supercritical multitype Markov branching processes

We consider multitype Markov branching processes with immigration occurring at time points generated by Poisson random measures. These models find applications to study evolution of multitype cell populations in which new cells join the population according to a time-varying immigration mechanism. T...

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Bibliographic Details
Published inStochastic models Vol. 39; no. 1; pp. 141 - 160
Main Authors Slavtchova-Bojkova, Maroussia, Hyrien, Ollivier, Yanev, Nikolay M.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.01.2023
Taylor & Francis Ltd
Subjects
Branching (mathematics)
Constraining
immigration
limiting distributions
Markov processes
Multitype branching processes
Poisson measures
Primary 60J80
Secondary 60F05
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Summary:We consider multitype Markov branching processes with immigration occurring at time points generated by Poisson random measures. These models find applications to study evolution of multitype cell populations in which new cells join the population according to a time-varying immigration mechanism. The focus of this paper is the supercritical case. We investigate the limiting behavior of the process for different rates of the Poisson random measures. In particular, we prove a result analogous to a strong LLN and establish limiting normal distributions.
ISSN:1532-6349
1532-4214
DOI:10.1080/15326349.2021.2016446