Today I read a paper titled “Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations”
The abstract is:
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.