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

• Published in: Stochastic models Vol. 18; no. 2; pp. 281 - 300
• Main Authors: Mitov, Kosto V., Yanev, Nickolay M.
• Format: Journal Article
• Language: English
• 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
• ISSN: 1532-6349; 1532-4214
• DOI: 10.1081/STM-120004468

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.