The Poisson-Dirichlet Distribution and Related Topics [electronic resource] : Models and Asymptotic Behaviors / by Shui Feng.
Tipo de material:
TextoSeries Probability and its ApplicationsEditor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010Descripción: XIV, 218 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642111945Trabajos contenidos: SpringerLink (Online service)Tema(s): Mathematics | Biology -- Mathematics | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Mathematical Biology in GeneralFormatos físicos adicionales: Sin títuloClasificación CDD: 519.2 Clasificación LoC:QA273.A1-274.9QA274-274.9Recursos en línea: de clik aquí para ver el libro electrónico Models -- The PoissonDirichlet Distribution -- The Two-Parameter PoissonDirichlet Distribution -- The Coalescent -- Stochastic Dynamics -- Particle Representation -- Asymptotic Behaviors -- Fluctuation Theorems -- Large Deviations for the PoissonDirichlet Distribution -- Large Deviations for the Dirichlet Processes.
The Poisson-Dirichlet distribution is an infinite dimensional probability distribution. It was introduced by Kingman over thirty years ago, and has found applications in a broad range of areas including Bayesian statistics, combinatorics, differential geometry, economics, number theory, physics, and population genetics. This monograph provides a comprehensive study of this distribution and some related topics, with particular emphasis on recent progresses in evolutionary dynamics and asymptotic behaviors. One central scheme is the unification of the Poisson-Dirichlet distribution, the urn structure, the coalescent, the evolutionary dynamics through the grand particle system of Donnelly and Kurtz. It is largely self-contained. The methods and techniques used in it appeal to researchers in a wide variety of subjects.
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