The Fokker-Planck equation : methods of solution and applications
The Fokker-Planck equation : methods of solution and applications
复制标题
DOI：
10.1007/978-3-642-96807-5
复制
发表时间：
1985-03
期刊：
影响因子：
--
通讯作者：
H. Risken
中科院分区：
文献类型：
--
作者：
H. Risken
如教派所示。3.1，2我们可以立即得到由线性朗之万方程(3.1，31)描述的过程的期望值。对于非线性朗之万方程(3.67,110)，期望值的获得要困难得多，因此这里我们首先推导出分布函数的方程。正如在引言中已经提到的，描述布朗运动的分布函数的微分方程首先是由Fokker[1.1]和Planck[1.2]推导的：现在已经有许多关于Fokker-Planck方程的评论文章和书籍[1.5-15]。
As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Langevin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function. As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived byFokker[1.1] andPlanck[1.2]: many review articles and books on the Fokker-Planck equation now exist [1.5 – 15].