摘要翻译：
本文利用泛函积分方法，结合状态变量均值和方差的运动方程，讨论了有色噪声作用下Langevin模型的动力学问题。研究了两组色噪声：(a)一种加性色噪声和一种乘性色噪声；(b)一种加性色噪声和两种乘性色噪声。研究情况(b)与最近关于包括随机兴奋性突触和抑制性突触和噪声输入的集成-激发模型的稳态阈下电压分布的争议有关。我们研究了线性朗之万模型的平稳概率分布和对时间相关（脉冲和正弦）输入的动力学响应。模型计算表明，FIM结果与直接模拟结果吻合较好。比较了各种近似解析解，如泛色噪声近似(UCNA)。文中指出，UCNA计算的脉冲和正弦输入的动力响应与DS和FIM计算的动力响应有很大的不同，尽管它们得到了相同的平稳分布。
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英文标题：
《Dynamics of the Langevin model subjected to colored noise:
  Functional-integral method》
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作者：
Hideo Hasegawa (Tokyo Gakugei Univ.)
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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英文摘要：
  We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is examined with the relevance to a recent controversy on the stationary subthreshold voltage distribution of an integrate-and-fire model including stochastic excitatory and inhibitory synapses and a noisy input. We have studied the stationary probability distribution and dynamical responses to time-dependent (pulse and sinusoidal) inputs of the linear Langevin model. Model calculations have shown that results of the FIM are in good agreement with those of direct simulations (DSs). A comparison is made among various approximate analytic solutions such as the universal colored noise approximation (UCNA). It has been pointed out that dynamical responses to pulse and sinusoidal inputs calculated by the UCNA are rather different from those of DS and the FIM, although they yield the same stationary distribution.
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PDF链接：
https://arxiv.org/pdf/708.2563