Łuczka J
Institute of Physics, University of Silesia, 40-007 Katowice, Poland.
Chaos. 2005 Jun;15(2):26107. doi: 10.1063/1.1860471.
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.
我们研究由热平衡或非平衡（非热）有色噪声驱动的经典非马尔可夫过程。给出了有色噪声的示例。对于由热平衡噪声驱动的过程，涨落耗散关系成立。因此，该系统必须由广义（积分 - 微分）朗之万方程描述，且对阻尼积分核有限制：其形式取决于噪声的相关函数。对于由非平衡噪声驱动的过程，不存在这样的限制：它们被认为由具有独立噪声项的随机微分（伊藤型或朗之万型）方程描述。对于后者，我们回顾由奥恩斯坦 - 乌伦贝克噪声驱动的一维系统的分析方法。
