Wang Peng, Tartakovsky Alexandre M, Tartakovsky Daniel M
Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
Phys Rev Lett. 2013 Apr 5;110(14):140602. doi: 10.1103/PhysRevLett.110.140602. Epub 2013 Apr 2.
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.
理解由具有有色噪声的朗之万方程描述的动力系统的介观行为是众多领域中的一项基本挑战。我们提出了一种新方法，用于推导状态变量的联合概率密度函数和边缘概率密度函数的闭式方程。该方法基于所谓的大涡扩散率闭合，可用于对由具有任意相关函数的噪声描述的一大类非马尔可夫过程进行建模。我们针对几个线性和非线性朗之万方程证明了所提出的概率密度函数方法的准确性。
