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Academic & Professional Books  Reference  Data Analysis & Modelling  Modelling

Probabilistic Models of Population Evolution Scaling Limits, Genealogies and Interactions

By: Étienne Pardoux(Author)
133 pages, 2 colour & 4 b/w illustrations, 4 colour tables
Publisher: Springer-Verlag
Probabilistic Models of Population Evolution
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  • Probabilistic Models of Population Evolution ISBN: 9783319303260 Paperback Jun 2016 Usually dispatched within 1-2 weeks
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About this book Contents Customer reviews Biography Related titles

About this book

This expository book presents the mathematical description of evolutionary models of populations subject to interactions (e.g. competition) within the population. The author includes both models of finite populations, and limiting models as the size of the population tends to infinity. The size of the population is described as a random function of time and of the initial population (the ancestors at time 0). The genealogical tree of such a population is given. Most models imply that the population is bound to go extinct in finite time. It is explained when the interaction is strong enough so that the extinction time remains finite, when the ancestral population at time 0 goes to infinity. The material could be used for teaching stochastic processes, together with their applications.

Contents

- Introduction
- Branching Processes
- Convergence to a Continuous State Branching Process
- Continuous State Branching Process (CSBP)
- Genealogies
- Models of Finite Population with Interaction
- Convergence to a Continuous State Model
- Continuous Model with Interaction
- Appendix

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Biography

Étienne Pardoux is Professor at Aix-Marseille University, working in the field of Stochastic Analysis, in particular Stochastic partial differential equations. He obtained his PhD in 1975 at University of Paris-Sud.

By: Étienne Pardoux(Author)
133 pages, 2 colour & 4 b/w illustrations, 4 colour tables
Publisher: Springer-Verlag
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