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.
Keywords
- Monotypic Population
- Martingale Property
- Poisson Point Measure
- Feller Diffusion
- Continuous State Branching Process
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAcknowledgements
The authors wish to warmly thank Amandine Véber for the reading of the manuscript and her suggestions.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)