scholarly journals Hamiltonian systems with Lévy noise: Symplecticity, Hamilton’s principle and averaging principle

2019 ◽  
Vol 398 ◽  
pp. 69-83 ◽  
Author(s):  
Pingyuan Wei ◽  
Ying Chao ◽  
Jinqiao Duan
Keyword(s):  
Hamiltonian Systems ◽  
Lévy Noise ◽  
Averaging Principle ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Levy Noise

An averaging principle for neutral stochastic fractional order differential equations with variable delays driven by Lévy noise

2021 ◽  
Author(s):  
Guangjun Shen ◽  
Jiang-Lun Wu ◽  
Ruidong Xiao ◽  
Xiuwei Yin
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lévy Noise ◽  
Averaging Principle ◽  
Fractional Order Differential Equations ◽  
Variable Delays ◽  
Fractional Differential ◽  
Stochastic Fractional Differential Equations ◽  
Levy Noise ◽  
Convergence In Mean

In this paper, we establish an averaging principle for neutral stochastic fractional differential equations with non-Lipschitz coefficients and with variable delays, driven by Lévy noise. Our result shows that the solutions of the equations concerned can be approximated by the solutions of averaged neutral stochastic fractional differential equations in the sense of convergence in mean square. As an application, we present an example with numerical simulations to explore the established averaging principle.

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