Denisov S I, Vitrenko A N, Horsthemke Werner
Department of Mechanics and Mathematics, Sumy State University, 2, Rimskiy-Korsakov Street, 40007 Sumy, Ukraine.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046132. doi: 10.1103/PhysRevE.68.046132. Epub 2003 Oct 28.
We study the role that the cross-correlation of noises plays in the statistical behavior of systems driven by two multiplicative Gaussian white noises. The temporal evolution of the system is described by a Langevin equation, for which we adopt a general interpretation that includes the Ito as well as the Stratonovich interpretation. We derive the stochastically equivalent Fokker-Planck equation by means of the two-stage averaging of a state-dependent function. Analyzing the stationary solution of the Fokker-Planck equation for specific examples, we show explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.
我们研究了噪声的互相关在由两个乘性高斯白噪声驱动的系统的统计行为中所起的作用。该系统的时间演化由一个朗之万方程描述，对此我们采用一种包含伊藤解释以及斯特拉托诺维奇解释的广义解释。我们通过对一个与状态有关的函数进行两阶段平均，推导出了随机等效的福克 - 普朗克方程。通过分析特定示例下福克 - 普朗克方程的平稳解，我们明确表明白噪声的互相关可以引发非平衡转变。
