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In this chapter, we model population dynamics whose individuals reproduce and die at random times, continuously in time, allowing overlapping generations characteristic of certain species. We study in detail the properties of the branching processes and of the birth and death processes. We also show how some approximations of these processes in large population lead to dynamical systems or stochastic differential equations.

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Continuous Time Population Processes

  • 章节

  • 发表日期：

    2026年

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  • Sylvie Méléard

摘要

In this chapter, we model population dynamics whose individuals reproduce and die at random times, continuously in time, allowing overlapping generations characteristic of certain species. We study in detail the properties of the branching processes and of the birth and death processes. We also show how some approximations of these processes in large population lead to dynamical systems or stochastic differential equations.