Abstract
This course concerns the stochastic modeling of population dynamics. In the first part, we focus on monotype populations described by one-dimensional stochastic differential equations with jumps. We consider their scaling limits for large populations and study the long time behavior of the limiting processes. It is achieved, thanks to martingale properties, Poisson measure representations, and stochastic calculus. These tools and results will be used and extended to measure-valued processes in the second part. The latter is dedicated to structured populations, where individuals are characterized by a trait belonging to a continuum.
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Acknowledgements
The authors wish to warmly thank Amandine Véber for the reading of the manuscript and her suggestions.
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© 2015 Springer International Publishing Switzerland
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Bansaye, V., Méléard, S. (2015). Introduction. In: Stochastic Models for Structured Populations. Mathematical Biosciences Institute Lecture Series(), vol 1.4. Springer, Cham. https://doi.org/10.1007/978-3-319-21711-6_1
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DOI: https://doi.org/10.1007/978-3-319-21711-6_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21710-9
Online ISBN: 978-3-319-21711-6
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