منابع مشابه
Branching Processes
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...
متن کاملBranching Processes
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...
متن کاملBranching Processes and Applications
These are notes of a talk given at the probability student seminar in the Weizmann institute of science on September 2011. After introducing Galton-Watson branching process, we consider conditions for which the process survives forever and for which it has a binary tree as a subtree with the same root. As an application, Mandelbrot’s fractal percolation model is discussed.
متن کاملSimple Branching Processes
Consider a particle that can replicate itself instantaneously at random times. In general there is a distribution of times from which the particle draws in order to initiate replication. For simplicity, we assume a Poisson process, and a replication rate of λ. Consider the total integer number of particles N(t) at any time t. Let us now consider one realization of the continuous-time branching ...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1948
ISSN: 0003-4851
DOI: 10.1214/aoms/1177730146