منابع مشابه
Branching 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 کاملBranching 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 Apert syndrome
Apert syndrome is a birth defect caused by mutation of either of two specific base pairs. The syndrome occurs at a rate of about 1 in 200,000 live births, much higher than the estimated 1 in 100,000,000 expected from the average estimated human mutation rate. Mutation rates do vary significantly across the genome (e.g. “hot spots”); but such a large variation is still very unexpected. It has al...
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ژورنال
عنوان ژورنال: Mathematical Economics
سال: 2015
ISSN: 1733-9707,2450-1131
DOI: 10.15611/me.2015.11.06