LIMIT THEOREMS FOR SUBCRITICAL MARKOV BRANCHING PROCESSES WITH NON-HOMOGENEOUS POISSON IMMIGRATION

This paper deals with Markov branching processes allowing immigration at random time points described by a non-homogeneous Poisson process. This class of processes generalizes a classical model proposed by Sevastyanov, which included a time-homogeneous Poisson immigration. The proposed model finds a...

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Published inComptes rendus de l'Academie bulgare des Sciences Vol. 68; no. 3; p. 313
Main Authors Hyrien, Ollivier, Mitov, Kosto V, Yanev, Nikolay M
Format Journal Article
LanguageEnglish
Published Bulgarian Academy of Sciences 01.01.2015
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Summary:This paper deals with Markov branching processes allowing immigration at random time points described by a non-homogeneous Poisson process. This class of processes generalizes a classical model proposed by Sevastyanov, which included a time-homogeneous Poisson immigration. The proposed model finds applications in cell kinetics studies. Limit theorems are obtained now in the subrcritical case. Some of these results extend the classical results derived by Sevastyanov, and others offer novel insights as a result of the non-homogeneity of the immigration process.Key words: branching processes, non-homogeneous Poisson immigration, cell kinetics, statistical inference2010 Mathematics Subject Classification: 60J80
ISSN:1310-1331