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PubMed · 16035909

Non-Markovian stochastic processes: colored noise.

J Łuczka
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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.

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ArtifactsBiophysical PhenomenaBiophysicsHot TemperatureMarkov ChainsModels, StatisticalModels, TheoreticalMultivariate AnalysisNormal DistributionPoisson DistributionStochastic ProcessesJournal ArticleResearch Support, Non-U.S. Gov't

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J Łuczka. 2005. Non-Markovian stochastic processes: colored noise.. https://doi.org/10.1063/1.1860471

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