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 → ∞ 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/√N. Consequences and relations to some previous approaches are outlined.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-1,
author = {Jens Christian Claussen},
title = {Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {17-31},
zbl = {1141.91329},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-1}
}
Jens Christian Claussen. Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations. Banach Center Publications, Tome 83 (2008) pp. 17-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc80-0-1/