title: Non-Markovian stochastic processes: colored noise.
abstract: We survey classical non-Markovian processes driven by thermal equilibrium or nonequilibrium (nonthermal) colored noise. Examples of colored noise are presented. For processes driven by thermal equilibrium noise, the fluctuation-dissipation relation holds. In consequence, the system has to be described by a generalized (integro-differential) Langevin equation with a restriction on the damping integral kernel: Its form depends on the correlation function of noise. For processes driven by nonequilibrium noise, there is no such a restriction: They are considered to be described by stochastic differential (Ito- or Langevin-type) equations with an independent noise term. For the latter, we review methods of analysis of one-dimensional systems driven by Ornstein-Uhlenbeck noise.
authors.affiliation: Institute of Physics, University of Silesia, 40-007 Katowice, Poland. luczka@us.edu.pl
authors.forename: J
authors.initials: J
authors.lastname: Łuczka
mesh_terms: D016477:Artifacts; D055592:Biophysical Phenomena; D001703:Biophysics; D006358:Hot Temperature; D008390:Markov Chains; D015233:Models, Statistical; D008962:Models, Theoretical; D015999:Multivariate Analysis; D016011:Normal Distribution; D016012:Poisson Distribution; D013269:Stochastic Processes