The branching process occuring at Poisson-distributed times implies that at infinitesimally small times ε, the number of particles issuing from a particular offspring is either one, or the number arising from a single branching event. For a subcritical branching process, mean generation size declines exponentially to zero. A branching process is said to be subcritical if <1, critical if =1, and supercritical if >1. birth-death process, branching process, immigration, progeny generating function, matrix exponential, Poisson process, Kronecker product, mutation, X-linked, haplotype, vaccination, HIV Disciplines Statistics and Probability Comments This preprint was published as Karin Dorman, Janet Sinsheimer, and Kenneth Lange, "In the Garden of For a supercritical process, mean generation size exhibits long-term exponential growth. An extension to “almost” regular graphs and a quenched version are also given. Full Record; Other Related Research Some of the example of stochastic process are Poisson process, renewal process, branching process, semi-Markov process, time-reversible Markov chains, birth–death process, random walks, and Brownian motion. OSTI.GOV Journal Article: Poisson branching point processes. Stochastic models could be discrete and continuous in time and state space. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers. the Poisson(1) branching process conditioned to survive forever. Poisson representations of branching Markov and measure-valued branching processes Thomas G. Kurtz ∗ Eliane Rodrigues† Departments of Mathematics and Statistics Instituto de Matem´aticas University of Wisconsin - Madison UNAM 480 Lincoln Drive M´exico, DF 04510 Madison, WI 53706-1388 Mexico kurtz@math.wisc.edu eliane@math.cinvestav.mx January 1, 2008 Abstract Representations of … Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Google Scholar ; 2. T. E. Harris, The Theory of Branching Processes (Springer, New York, 1963). 1. REFERENCES. 1. Poisson branching point processes.

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