论文标题
非线性1D-SDE的最佳FPE。 I：加性高斯颜色噪音
Optimal FPE for non-linear 1d-SDE. I: Additive Gaussian colored noise
论文作者
论文摘要
对于感兴趣的变量，可以通过某些投影过程将许多在物理，化学，生物学，金融等中发生的复杂现象降低到1-D随机微分方程（SDE）。通常，此SDE既是非线性的，也是非马克维亚人，因此对于概率密度函数（PDF），Fokker Planck方程（FPE）通常是无法获得的。但是，FPE是可取的，因为它是获得相关的分析统计信息的主要工具，例如固定PDF和第一个通行时间。过去，许多作者已经解决了这个问题，但是由于对交互作用图片的使用不正确（获得降低的FPE的标准工具）先前的理论结果是不正确的，如SDE的直接数值模拟所证实。通常，我们将展示如何解决该问题，我们将从扰动方法中得出正确的最佳FPE。遵循的方法和所获得的结果具有一般有效性，超出了此处用作指数相关的高斯驾驶的简单情况。它们甚至可以应用于具有通用时间相关的非高斯驱动器。
Many complex phenomena occurring in physics,chemistry, biology, finance, etc. can be reduced, by some projection process, to a 1-d stochastic Differential Equation (SDE) for the variable of interest. Typically, this SDE is both non-linear and non-markovian, so a Fokker Planck equation (FPE), for the probability density function (PDF), is generally not obtainable. However, a FPE is desirable because it is the main tool to obtain relevant analytical statistical information such as stationary PDF and First Passage Time. This problem has been addressed by many authors in the past, but due to an incorrect use of the interaction picture (the standard tool to obtain a reduced FPE) previous theoretical results were incorrect, as confirmed by direct numerical simulation of the SDE. We will show, in general, how to address the problem and we will derived the correct best FPE from a perturbation approach. The method followed and the results obtained have a general validity beyond the simple case of exponentially correlated Gaussian driving used here as an example; they can be applied even to non Gaussian drivings with a generic time correlation.
