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math.DS2016
Governing equations for Probability densities of stochastic differential equations with discrete time delays
Yayun Zheng, Xu Sun
The time evolution of probability densities for solutions to stochastic differential equations (SDEs) without delay is usually described by Fokker-Planck equations, which require t…
math.DS2012
Modeling nonlinear random vibration: Implication of the energy conservation law
Xu Sun, Jinqiao Duan, Xiaofan Li
Nonlinear random vibration under excitations of both Gaussian and Poisson white noises is considered. The model is based on stochastic differential equations, and the corresponding…
math.DS2012
An alternative expression of Di Paola and Falson's formula for stochastic dynamics
Xu Sun, Jinqiao Duan, Xiaofan Li
Di Paola and Falsone's formula is widely used in studying stochastic dynamics of nonlinear systems under Poisson white noise. In this short communication, an alternative expression…