Our model is Markov in nature, and would involve branching processes
with immigration and emigration.
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.
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.
Our analysis is based on branching processes
with time-dependent rates, in which both branching and extinction happen randomly, and all the existing taxa are independent of each other.
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
in the analysis of the height of trees.
Karlin, Embedding of urn schemes into continuous time Markov branching processes
and related limit theorems.