Cell contamination and branching processes in a random environment with immigration

DOI10.1239/aap/1261669586zbMath1202.92023arXiv0805.1863OpenAlexW4390770600MaRDI QIDQ3558938

Vincent Bansaye

Publication date: 11 May 2010

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.1863

zbMATH Keywords

renewal theoremempirical measuresMarkov chains indexed by a tree

Mathematics Subject Classification ID

Epidemiology (92D30) Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Applications of branching processes (60J85) Population dynamics (general) (92D25) Processes in random environments (60K37) Cell biology (92C37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

• Proliferating parasites in dividing cells: Kimmel's branching model revisited
• Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment
• Markov chains indexed by trees
• Limit theorems for subcritical branching processes in random environment.
• Criticality for branching processes in random environment
• A note on multitype branching processes with immigration in a random environment
• Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
• On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment
• Some limit theorems for positive recurrent branching Markov chains: I
• Some limit theorems for positive recurrent branching Markov chains: II
• On Branching Processes in Random Environments
• On Branching Processes with Random Environments: I: Extinction Probabilities
• Branching Processes with Random Environments, II: Limit Theorems
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