Path-valued branching processes and nonlocal branching superprocesses
نویسندگان
چکیده
منابع مشابه
Poisson representations of branching Markov and measure-valued branching processes
Representations of measure-valued processes in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a “level,” but unlike earlier constructions, the levels change with time. In fact, death of a particle occurs only when the level of the particle hits infinity. For each time t the joint distribution of l...
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Representations of branching Markov processes and their measurevalued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a “level,” but unlike earlier constructions, the levels change with time. In fact, death of a particle occurs only when the level of the particle crosses a specified level...
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A theorem of Evans and Perkins (1991) on the absolute continuity of distributions of Dawson-Watanabe superprocesses is extended to general branching mechanisms. This result is then used to establish the propagation properties of the superprocesses following Evans and Perkins (1991) and Perkins (1990).
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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...
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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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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2014
ISSN: 0091-1798
DOI: 10.1214/12-aop759