Sample paths of continuous-state branching processes with dependent immigration

We prove the existence and pathwise uniqueness of the solution to a stochastic integral equation driven by Poisson random measures based on Kuznetsov measures for a continuous-state branching process. That gives a direct construction of the sample path of a continuous-state branching process with de...

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Bibliographic Details
Published inStochastic models Vol. 35; no. 2; pp. 167 - 196
Main Author Li, Zenghu
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2019
Taylor & Francis Ltd
Subjects
Branching (mathematics)
Continuous-state branching process
dependent immigration
Immigration
Integral equations
Markov analysis
Markov processes
Poisson random measure
stochastic equation
Yamada-Watanabe type condition
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ISSN1532-6349
1532-4214
DOI10.1080/15326349.2019.1575753

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Summary:We prove the existence and pathwise uniqueness of the solution to a stochastic integral equation driven by Poisson random measures based on Kuznetsov measures for a continuous-state branching process. That gives a direct construction of the sample path of a continuous-state branching process with dependent immigration. The immigration rates depend on the population size via some functions satisfying a Yamada-Watanabe type condition. We only assume the existence of the first moment of the process. The existence of excursion law for the continuous-state branching process is not required. By special choices of the ingredients, we can make changes in the branching mechanism or construct models with competition.
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ISSN:1532-6349
1532-4214
DOI:10.1080/15326349.2019.1575753