27 citations · 46 across the 11 of their papers we have counts for
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A representation formula for the probability density in stochastic dynamical systems with memory
Fang Yang, Xu Sun
Marcus stochastic delay differential equations (SDDEs) are often used to model stochastic dynamical systems with memory in science and engineering. Since no infinitesimal generator…
On the abrupt change of the maximum likelihood state in a simplified stochastic thermohaline circulation system
Fang Yang, Xu Sun, Jinqiao Duan
The maximum likelihood state for a simplified stochastic thermohaline circulation model is investigated. It is shown that a jump occurs for the maximum likelihood state during tran…
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…
Fokker-Planck equations for Marcus stochastic differential equations driven by Levy processes
Xu Sun, Xiaofan Li, Yayun Zheng
Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Levy processes and have wide applications in en…
Derivation of Fokker-Planck equations for stochastic dynamical systems under excitation of multiplicative non-Gaussian white noise
Xu Sun, Jinqiao Duan, Xiaofan Li +3
Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of unce…
State estimation under non-Gaussian Levy noise: A modified Kalman filtering method
Xu Sun, Jinqiao Duan, Xiaofan Li +1
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail…