Titlebook: Probabilistic Models of Population Evolution; Scaling Limits, Gene Étienne Pardoux Textbook 2016 Springer International Publishing Switzerl

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Convergence to a Continuous State Model, and ., respectively. In section ., we shall take the limit in the model for the evolution of the population size, as a function of the two parameters . (the ancestral population size) and . (time). Since we want to stick to our rather minimal assumptions on the function ., checking tightness requir

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Models of Finite Population with Interaction,birth naturally at rate . and dies naturally at rate .. Moreover, we suppose that each individual gives birth and dies because of interaction with others at rates which depend upon the current population size. We exclude multiple births at any given time and we define the interaction rule through a continuous function . which again satisfies

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