Abstract
Under a non-Lipschitz condition, the averaging principle for the general stochastic differential delay equations (SDDEs) is established. The solutions of convergence in mean square and convergence in probability between standard SDDEs and the corresponding averaged SDDEs are considered.MSC:34K50, 34C29.
Highlights
1 Introduction The averaging principle plays an important role in dynamical systems in problems of mechanics, physics, control and many other areas
As a special non-Gaussian Lévy noise, Poisson noise is usually a hot spot when dealing with stochastic systems
Stoyanov and Bainov [ ] investigated the averaging method for a class of stochastic differential equations with Poisson noise. They considered the connections between the solutions of a standard form and the solutions of averaged systems and proved that under some conditions the solutions of averaged systems converge to the solutions of original systems in mean square and in probability
Summary
The averaging principle plays an important role in dynamical systems in problems of mechanics, physics, control and many other areas. Instead of Poisson noise, Xu et al [ ] established an averaging principle for stochastic differential equations with general non-Gaussian Lévy noise. Motivated by the previous paper, we consider the averaging principles for general SDEs and SDDEs with a non-Lipschitz condition.
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