Branching within branching: a model for host-parasite co-evolution

DOI10.1016/j.spa.2015.12.007zbMath1336.60164OpenAlexW2270080115MaRDI QIDQ271859

Sören Gröttrup, Gerold Alsmeyer

Publication date: 20 April 2016

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2015.12.007

zbMATH Keywords

extinction probabilityrandom environmentbranching-within-branching modelextinction-explosion principleGalton-Watson processHeyde-Seneta norminghost-parasite co-evolutioninfinite random cell linerandom treesize-biasing

Mathematics Subject Classification ID

Applications of branching processes (60J85) Population dynamics (general) (92D25) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items

Parasite infection in a cell population with deaths and reinfections, Spread of parasites affecting death and division rates in a cell population

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence in law of the minimum of a branching random walk
• Size-biased branching population measures and the multi-type \(x \log x\) condition
• Detection of cellular aging in a Galton-Watson process
• Limit theorems for Markov processes indexed by continuous time Galton-Watson trees
• Proliferating parasites in dividing cells: Kimmel's branching model revisited
• Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
• A necessary and sufficient condition for noncertain extinction of a branching process in a random environment (BPRE)
• Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment
• A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means
• Uniform convergence of martingales in the branching random walk
• The first birth problem for an age-dependent branching process
• Limit theorems for branching processes in a random environment
• Normalizing constants for branching processes in random environments (B.P.R.E.)
• The supercritical Galton-Watson process in varying environments -- Seneta-Heyde norming
• Seneta-Heyde norming in the branching random walk
• Limit theorems for subcritical branching processes in random environment.
• Change of measures for Markov chains and the \(L\log L\) theorem for branching processes
• Criticality for branching processes in random environment
• Conceptual proofs of \(L\log L\) criteria for mean behavior of branching processes
• On the survival probability of a branching process in a random environment
• Minima in branching random walks
• Surviving particles for subcritical branching processes in random environment
• One-dimensional linear recursions with Markov-dependent coefficients
• Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging
• Functional limit theorems for strongly subcritical branching processes in random environment
• On weighted branching processes in random environment.
• A Host-Parasite Model for a Two-Type Cell Population
• Branching Feller diffusion for cell division with parasite infection
• Cell contamination and branching processes in a random environment with immigration
• Multitype Bienaymé–Galton–Watson processes escaping extinction
• On the extinction times of varying and random environment branching processes
• Martingale convergence in the branching random walk
• Chernoff's theorem in the branching random walk
• Growth rates in the branching random walk
• The xlogx condition for general branching processes
• Measure change in multitype branching
• Limit Theorem for an Intermediate Subcritical Branching Process in a Random Environment
• A cascade decomposition theory with applications to Markov and exchangeable cascades
• Elementary new proofs of classical limit theorems for Galton–Watson processes
• On the Waiting Time to Escape
• On Branching Processes in Random Environments
• Extensions of a Limit Theorem of Everett, Ulam and Harris on Multitype Branching Processes to a Branching Process with Countably Many Types
• On Branching Processes with Random Environments: I: Extinction Probabilities
• Branching Processes with Random Environments, II: Limit Theorems
• Probability
• Branching processes in biology