2000 character limit reached
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations (0803.2443v1)
Published 17 Mar 2008 in q-bio.PE, cond-mat.stat-mech, cs.SI, math.PR, math.ST, physics.bio-ph, physics.soc-ph, and stat.TH
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.