An averaging principle for stochastic dynamical systems with Lévy noise

2011 ◽  
Vol 240 (17) ◽  
pp. 1395-1401 ◽  
Author(s):  
Yong Xu ◽  
Jinqiao Duan ◽  
Wei Xu
Keyword(s):  
Dynamical Systems ◽  
Lévy Noise ◽  
Averaging Principle ◽  
Stochastic Dynamical Systems ◽  
Levy Noise

Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

2019 ◽  
Vol 17 (03) ◽  
pp. 477-511 ◽  
Author(s):  
Shenglan Yuan ◽  
Jianyu Hu ◽  
Xianming Liu ◽  
Jinqiao Duan
Keyword(s):  
Biological Sciences ◽  
Dynamical Systems ◽  
Scale Parameter ◽  
Lévy Noise ◽  
Stochastic Dynamical Systems ◽  
Time Dynamics ◽  
Slow Manifolds ◽  
Long Time ◽  
Non Gaussian ◽  
Levy Noise

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, and then we eliminate the fast variables to reduce the dimensions of these stochastic dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps to investigate long time dynamics. The approximations of slow manifolds with error estimate in distribution are also established. Furthermore, we corroborate these results by three examples from biological sciences.

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.

Sign in / Sign up

Export Citation Format

Share Document