Probability density function method for Langevin equations with colored noise.
Probability density function method for Langevin equations with colored noise.
复制标题
DOI：
10.1103/physrevlett.110.140602
复制
发表时间：
2013-04
影响因子：
8.6
通讯作者：
Peng Wang;A. Tartakovsky;D. Tartakovsky
中科院分区：
文献类型：
--
作者：
Peng Wang;A. Tartakovsky;D. Tartakovsky
理解由带色噪声的朗之万方程描述的动力学系统的介观行为是各个领域的一个基本挑战。我们提出了一种新的方法来获得封闭形式的方程的联合和边际概率密度函数的状态变量。这种方法是基于一个所谓的大涡扩散封闭，可以用来模拟一个广泛的类的非马尔可夫过程所描述的噪声与任意的相关函数。我们证明了几个线性和非线性Langevin方程的概率密度函数方法的准确性。
Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise is a fundamental challenge in a variety of fields. We propose a new approach to derive closed-form equations for joint and marginal probability density functions of state variables. This approach is based on a so-called large-eddy-diffusivity closure and can be used to model a wide class of non-Markovian processes described by the noise with an arbitrary correlation function. We demonstrate the accuracy of the proposed probability density function method for several linear and nonlinear Langevin equations.