Model biological population by branching processes
نویسندگان
چکیده
منابع مشابه
Model Checking Stochastic Branching Processes
Stochastic branching processes are a classical model for describing random trees, which have applications in numerous fields including biology, physics, and natural language processing. In particular, they have recently been proposed to describe parallel programs with stochastic process creation. In this paper, we consider the problem of model checking stochastic branching process. Given a bran...
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Galton-Watson processes were introduced by Francis Galton in 1889 as a simple mathematical model for the propagation of family names. They were reinvented by Leo Szilard in the late 1930s as models for the proliferation of free neutrons in a nuclear fission reaction. Generalizations of the extinction probability formulas that we shall derive below played a role in the calculation of the critica...
متن کاملBranching Processes
The study of branching processes began in the 1840s with Irénée-Jules Bienaymé, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician. In 1873, Galton sent a problem to the Educational Times regarding the survival of family names. When he did not receive a satisfactory answe...
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We introduce the basic theory of Galton-Watson branching processes, and the probabilistic tools needed to analyse them. The aim is to give a basic treatment of branching processes, including results on the limiting behaviour for subcritical, critical, and supercritical processes. We introduce just enough probabilistic theory to make the results rigourous, but avoid unnecessary technicalities as...
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Branching processes are a well-established tool in mathematical biology used to study the dynamics of rarefied populations where agents act independently and small stochastic density-independent changes in population sizes. However, they are often avoided by non-mathematicians because of their reliance on generating functions. Generating functions are powerful computational aids but are often d...
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ژورنال
عنوان ژورنال: Biomath Communications
سال: 2017
ISSN: 2367-5241,2367-5233
DOI: 10.11145/bmc.2017.01.161