منابع مشابه
Immortal Particle for a Catalytic Branching Process†
We study the existence and some asymptotic properties of a conservative branching particle system for which birth and death are triggered by contact with a set. Sufficient conditions for the process to be non-explosive are given, solving a long standing open problem. With probability one, it is shown that only one ancestry survives. In special cases, the evolution of the surviving particle is s...
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The immortal branching Markov process (iBMP) is a modification of the usual branching model, in which each particle of generation n is counted, in addition to its offspring, as a member of generation n + 1, its state being unchanged. When the number of offspring is Bernoulli, iBMP accounts, for instance, for the variability of the biological sequences that are produced by polymerase chain react...
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...
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ژورنال
عنوان ژورنال: Physica A: Statistical Mechanics and its Applications
سال: 2021
ISSN: 0378-4371
DOI: 10.1016/j.physa.2021.125853