Dimension-reduction of FPK equation via equivalent drift coefficient  

作　　者：Jianbing Chen Peihui Lin 

机构地区：[1]State Key Laboratory of Disaster Reduction in Civil Engineering & School of Civil Engineering, Tongji University

出　　处：《Theoretical & Applied Mechanics Letters》2014年第1期16-21,共6页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China(11172210);the Shuguang Program of Shanghai City(11SG21)

摘　　要：The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.

关 键 词：FPK equation drift coefficient probability density evolution method flux of probability nonlinear systems 

分 类 号：O175[理学—数学] O313[理学—基础数学]