Probabilistic Models of Population Evolution

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.

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.

"This book presents the mathematical description of evolutionary models of populations subject to interactions within the population. ... For readers' convenience, the book contains an appendix summarizing the necessary backgrounds and technical results on stochastic calculus. The materials are presented with clarity, brevity and styles. ... The book provides nice supplementary material for courses in stochastic processes and stochastic calculus." (Chao Zhu, Mathematical Reviews, April, 2017)

"The main originality of the book is the fact that it describes the evolution of a population where the birth or death rates of the various individuals are affected by the size of the population. ... The book is mainly intended to readers with some basic knowledge of stochastic processes and stochastic calculus. All in all, this is a serious piece of work." (Marius Iosifescu, zbMATH 1351.92003, 2017)