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Particle Representations for Measure-Valued Population Models
Ist Teil von
The Annals of probability, 1999-01, Vol.27 (1), p.166-205
Ort / Verlag
Institute of Mathematical Statistics
Erscheinungsjahr
1999
Link zum Volltext
Quelle
EZB-FREE-00999 freely available EZB journals
Beschreibungen/Notizen
Models of populations in which a type or location, represented by a point in a metric space E, is associated with each individual in the population are considered. A population process is neutral if the chances of an individual replicating or dying do not depend on its type. Measure-valued processes are obtained as infinite population limits for a large class of neutral population models, and it is shown that these measure-valued processes can be represented in terms of the total mass of the population and the de Finetti measures associated with an E∞-valued particle model X = (X1, X2,...) such that, for each t ≥ 0, (X1(t), X2(t),...) is exchangeable. The construction gives an explicit connection between genealogical and diffusion models in population genetics. The class of measure-valued models covered includes both neutral Fleming-Viot and Dawson-Watanabe processes. The particle model gives a simple representation of the Dawson-Perkins historical process and Perkins's historical stochastic integral can be obtained in terms of classical semimartingale integration. A number of applications to new and known results on conditioning, uniqueness and limiting behavior are described.