Branching Stochastic Evolutionary Models of Cell Populations
AbstractThis review paper surveys results on branching stochastic models with and without immigration published during the past nine years. Studies of this class of stochastic models were motivated by the quantitative analysis of the dynamics of population of cells of the central nervous system, called the terminally differentiated oligodendrocytes, and their progenitor cells. We focus on original ideas
specifically developed for Sevastyanov branching processes allowing the contribution of an external cellular compartment (e.g., stem cells) via a
nonhomogeneous Poisson immigration process. Limiting distributions are discribed in the subcritical, critical and supercritical cases for various immigration rates.
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