branching process

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branching process

[′branch·iŋ ′präs·əs]
(statistics)
A stochastic process in which the members of a population may have offspring and the lines of descent branch out as the new members are born.
References in periodicals archive ?
Janson, Functional limit theorems for multitype branching processes and generalized Pelya urns.
Karlin, Embedding of urn schemes into continuous time Markov branching processes and related limit theorems.
In this scenario, theory from subcritical branching processes (19), also known as mortal branching processes (20), guarantees that an outbreak will eventually die out, although perhaps not before a substantial number of transmissions occur.
We also applied the theory of branching processes with a negative binomial offspring distribution to estimate the probability that new introductions would lead to outbreaks exceeding various sizes.
Among them are a simple numerical approach to the Riemann hypothesis, aunifying construction for measure-valued continuous and discrete branching processes, examples of quantitative universal approximation, harmonic mappings with quadilateral image, meromorphic approximation on noncompact Riemann surfaces, a family of outer functions, the universality of series in Banach space, recent progress on fine differentiability and fine harmonicity, reversibility questions in groups arising from analysis, and the generalized binomial theorem.
Some reporting their own research and others surveying the literature, they cover record statistics, characterizing distributions through bivariate regression on differences of records, regenerative branching processes, conditional limit theorems for a continuous time and state branching process, large families and exceedances in branching processes, offspring extremes in branching processes, and statistical inferences for branching processes.
In this article, we show how to link stochastic L-systems to multitype branching processes, in order to characterize the probability distributions and moments of the numbers of organs in plant structure.
The objective of this article is to explore the relationship between stochastic L-Systems and multi-type branching processes in order to compute the corresponding probability generating functions and the distribution moments of the number of organs.
Most importantly, branching processes failed that would normally be needed to rotate the branching process into the third dimension--essential to developing a three-dimensional organ.
Recently a number of papers appeared (see, for instance, (1),(10), (12)-(19)) dealing with branching processes in random environment in which individuals reproduce independently of each other according to random offspring distributions which vary from one generation to the other.
Keywords: branching processes in random environment, survival probability, limit theorems, random walks
The main purpose of this note is to show how the same result can be derived quite elegantly and even extended to the nonlattice case within the theory of weighted branching processes.