Stochastic Models for Structured Populations

Vincent Bansaye is Associate Professor at Ecole Polytechnique in France and is a specialist of branching processes, particularly branching processes in random environments. Sylvie Méléard is Full Professor at Ecole Polytechnique in France and is a specialist of random particle systems and their large number approximations models for physics and biology.

• Introduction.- Discrete Monotype Population Models and One-dimensional Stochastic Differential Equations.- Birth and Death Processes.- Scaling Limits for Birth and Death Processes.- Continuous State Branching Processes.- Feller Diffusion with Random Catastrophes.- Structured Populations and Measure-valued Stochastic Differential Equations.- Population Point Measure Processes.- Scaling limits for the individual-based process.- Splitting Feller Diffusion for Cell Division with Parasite Infection.- Markov Processes along Continuous Time Galton-Watson Trees.- Appendix.

"It deals mainly with the study of the limiting behavior under different scaling limits of several types of continuous-time individual based models of population dynamics subjected to demographic stochasticity ... . The reader interested in the subject finds in this book very interesting results and a very well organized account on the state of the art, which integrates the main contributions of the authors and many other researchers in the (mostly recent) literature." (Carlos A. Braumann, zbMATH 1333.92004, 2016)