Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Volume 80 / 2008
Banach Center Publications 80 (2008), 17-31
MSC: Primary 91A22; Secondary 60J20, 92D50, 92D15.
DOI: 10.4064/bc80-0-1
Abstract
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.
