Er Guo-Kang, Iu Vai Pan
Faculty of Science and Technology, University of Macau, Macau Special Administrative Region, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):067701. doi: 10.1103/PhysRevE.85.067701. Epub 2012 Jun 20.
The state-space-split method for solving the Fokker-Planck-Kolmogorov equations in high dimensions is extended to solving the generalized Fokker-Planck-Kolmogorov equations in high dimensions for stochastic dynamical systems with a polynomial type of nonlinearity and excited by Poissonian white noise. The probabilistic solution of the motion of the stretched Euler-Bernoulli beam with cubic nonlinearity and excited by uniformly distributed Poissonian white noise is analyzed with the presented solution procedure. The numerical analysis shows that the results obtained with the state-space-split method together with the exponential polynomial closure method are close to those obtained with the Monte Carlo simulation when the relative value of the basic system relaxation time and the mean arrival time of the Poissonian impulse is in some limited range.
用于求解高维福克 - 普朗克 - 柯尔莫哥洛夫方程的状态空间分裂方法被扩展到求解具有多项式类型非线性且由泊松白噪声激励的高维广义福克 - 普朗克 - 柯尔莫哥洛夫方程，该方程用于随机动力系统。利用所提出的求解过程分析了具有三次非线性且由均匀分布的泊松白噪声激励的拉伸欧拉 - 伯努利梁运动的概率解。数值分析表明，当基本系统弛豫时间与泊松脉冲平均到达时间的相对值在一定有限范围内时，使用状态空间分裂方法结合指数多项式封闭方法得到的结果与蒙特卡罗模拟得到的结果相近。
