Approximate solution of the Fokker–Planck–Kolmogorov equation

作者: M. Di Paola , A. Sofi

DOI: 10.1016/S0266-8920(02)00034-6

关键词: Multiplicative functionProbability density functionWhite noiseMathematical physicsMathematicsMultiplicative noiseGaussian noiseWeightingFokker–Planck equationApplied mathematicsNonlinear system

摘要: … The Kolmogorov forward and backward equations, ruling the state transition PDF of the response, are parabolic partial differential equations … : the iterative procedure based on the …

参考文章(36)
Kiyosi Itô, On a Formula Concerning Stochastic Differentials Nagoya Mathematical Journal. ,vol. 3, pp. 55- 65 ,(1951) , 10.1017/S0027763000012216
Pol D. Spanos, J. B. Roberts, Random vibration and statistical linearization ,(1990)
M. Di Paola, G. Ricciardi, M. Vasta, A method for the probabilistic analysis of nonlinear systems Probabilistic Engineering Mechanics. ,vol. 10, pp. 1- 10 ,(1995) , 10.1016/0266-8920(95)91891-U
C. Soize, Steady state solution of Fokker-Planck equation in higher dimension Probabilistic Engineering Mechanics. ,vol. 3, pp. 196- 206 ,(1988) , 10.1016/0266-8920(88)90012-4
G.Q. Cai, Y.K. Lin, Exact and approximate solutions for randomly excited MDOF non-linear systems International Journal of Non-linear Mechanics. ,vol. 31, pp. 647- 655 ,(1996) , 10.1016/0020-7462(96)00053-4
R.S. Langley, A finite element method for the statistics of non-linear random vibration Journal of Sound and Vibration. ,vol. 101, pp. 41- 54 ,(1985) , 10.1016/S0022-460X(85)80037-7
K. Sobczyk, J. Trcebicki, Approximate probability distributions for stochastic systems: maximum entropy method Computer Methods in Applied Mechanics and Engineering. ,vol. 168, pp. 91- 111 ,(1999) , 10.1016/S0045-7825(98)00135-2
G.Q. Cai, Y.K. Lin, I. Elishakoff, A new approximate solution technique for randomly excited non-linear oscillators—II International Journal of Non-linear Mechanics. ,vol. 27, pp. 969- 979 ,(1992) , 10.1016/0020-7462(92)90049-D