有限和无限种群中协同进化动力学的离散随机过程、复制子和Fokker-Planck方程
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
摘要：
共同进化动力学中的小尺度波动出现在生物学以及社会和经济系统的模型中。这个简短的教程回顾调查从一个随机过程离散的时间和状态的系统方法。无限总体的极限$N\to \infty$可以被明确地考虑，通常导致零阶的复制型方程，以及$1/\sqrt{N}$中的一阶的Fokker-Planck型方程。概述了一些以前的方法的后果和关系。
英文摘要：
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit $N\to \infty$ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in $1/\sqrt{N}$. Consequences and relations to some previous approaches are outlined.
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