Analytical and numerical studies of multiplicative noise
Analytical and numerical studies of multiplicative noise
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DOI：
10.1103/physreva.26.1589
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发表时间：
1982-09
影响因子：
2.9
通讯作者：
J. M. Sancho;M. S. Miguel;S. Katz;J. Gunton
中科院分区：
文献类型：
--
作者：
J. M. Sancho;M. S. Miguel;S. Katz;J. Gunton
我们考虑随机微分方程的一个变量q乘白色和非白色（“有色”）噪声适当的描述非平衡系统的经验波动，这不是”自我起源。“我们讨论了模拟这些方程的数值算法，以及另一种分析处理。特别地，我们通过分析噪声的相关时间τ的幂次展开，导出了过程概率密度的近似Fokker-Planck方程。我们还讨论了这些方程的定态解。我们已经应用我们的数值和分析方法的“Stratonovich模型”经常在文献中使用的研究非平衡系统。数值分析证实了分析预测的时间无关的属性。我们表明，对于大的噪声强度D的平稳分布发展的峰值增加τ成为主导的大-τ极限。数值分析了该过程在稳态下的关联时间。我们发现在相关时间作为D和τ的函数增加的意义上的”减慢”。这一结果表明了斯特拉托诺维奇早期分析的错误。
We consider stochastic differential equations for a variable q with multiplicative white and nonwhite (" colored") noise appropriate for the description of nonequilibrium systems which experience fluctuations which are not" self-originating." We discuss a numerical algorithm for the simulation of these equations, as well as an alternative analytical treatment. In particular, we derive approximate Fokker-Planck equations for the probability density of the process by an analysis of an expansion in powers of the correlation time τ of the noise. We also discuss the stationary solution of these equations. We have applied our numerical and analytical methods to the" Stratonovich model" often used in the literature to study nonequilibrium systems. The numerical analysis corroborates the analytical predictions for the time-independent properties. We show that for large noise intensity D the stationary distribution develops a peak for increasing τ that becomes dominant in the large-τ limit. The correlation time of the process in the steady state has been analyzed numerically. We find a" slowing down" in the sense that the correlation time increases as a function of both D and τ.. This result shows the incorrectness of an earlier analysis of Stratonovich.