Critical Bellman-Harris branching processes with infinite variance allowing state-dependent immigration

The branching processes with state-dependent immigration are considered as alternating regenerative processes. The main purpose is to demonstrate some new "regenerative" methods. Critical Bellman-Harris branching processes with state-dependent immigration are investigated and new limit the...

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Bibliographic Details
Published inStochastic models Vol. 18; no. 2; pp. 281 - 300
Main Authors Mitov, Kosto V., Yanev, Nickolay M.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 30.05.2002
Taylor & Francis
Subjects
Age-dependent branching processes
Alternating regenerative processes
AMS Subject Classification: Primary 60J80; Secondary 60F05
Exact sciences and technology
Infinite mean cycles
Limit theorems
Limiting distributions
Linear inference, regression
Markov processes
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
State-dependent immigration
Statistics
Branching process
Renewal process
Immigration
Age dependence
Asymptotic distribution
State dependence
Regenerative process
Stochastic process
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ISSN1532-6349
1532-4214
DOI10.1081/STM-120004468

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Summary:The branching processes with state-dependent immigration are considered as alternating regenerative processes. The main purpose is to demonstrate some new "regenerative" methods. Critical Bellman-Harris branching processes with state-dependent immigration are investigated and new limit theorems are obtained in the case of an infinite offspring variance and possibly infinite mean of the immigrants.
ISSN:1532-6349
1532-4214
DOI:10.1081/STM-120004468