Dimension-reduction of FPK equation via equivalent drift coefficient

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 excite...

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Bibliographic Details
Published in:Theoretical and applied mechanics letters 2014, Vol.4 (1), p.16-21, Article 013002
Main Authors: Chen, Jianbing, Lin, Peihui
Format: Article
Language:English
Subjects:
drift coefficient
flux of probability
FPK equation
FPK方程
nonlinear systems
probability density evolution method
加性白噪声
密度演化方程
概率密度演化方法
漂移系数
等效系数
降维
非线性随机动力学
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Summary: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.
ISSN:2095-0349
2095-0349
DOI:10.1063/2.1401302