@inbook{35ceeee759be4877952edbd66e741cf7,

title = "The Bellman–Harris Process",

abstract = "The Bellman–Harris branching process is more general than the processes considered in the preceding chapters. Lifetimes of particles are nonnegative random variables with arbitrary distributions. It is described as follows. A single ancestor particle is born at t = 0. It lives for time τ which is a random variable with cumulative distribution function (Formula Presented). At the moment of death, the particle produces a random number of progeny according to a probability distribution with pgf f(s). Each of the first generation progeny behaves, independently of each other and the ancestor, as the ancestor particle did, i.e., it lives for a random time distributed according to (Formula Presented) and produces a random number of progeny according to f(s). If we denote Z(t) the particle count at time t, we obtain a stochastic process (Formula Presented). This so-called age-dependent process is generally non-Markov, but two of its special cases are Markov: the Galton–Watson process and the age-dependent branching process with exponential lifetimes. The Bellman–Harris process is more difficult to analyze, but it has many properties similar to these two processes.",

keywords = "Cell Cycle Duration, Cell Cycle Phase, Cell Cycle Time, Renewal Equation, Watson Process",

author = "Marek Kimmel and Axelrod, {David E.}",

note = "Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media, LLC.",

year = "2015",

doi = "10.1007/978-1-4939-1559-0_5",

language = "English (US)",

series = "Interdisciplinary Applied Mathematics",

publisher = "Springer Nature",

pages = "87--105",

booktitle = "Interdisciplinary Applied Mathematics",

address = "United States",

}