一类带脉冲的分数阶中立型随机微分方程的平均值原理

Averaging Principle for a Class of Fractional Neutral Stochastic Differential Equations with Impulses

平均值原理作为简化动力系统的一个强有力的工具,使得在更真实的复杂模型和更易于分析和模拟的简单模型之间找到平衡.文章主要讨论一类带脉冲的Lévy噪声驱动的分数阶中立型随机微分方程的平均值原理,通过逐次逼近的方法保证解的存在唯一性,并证明均值化方程的解在均方和依概率意义下收敛到原方程的解.

As a powerful tool to simplify the dynamic system,the mean value principle finds a balance between more real complex models and simple models that is easier to analyze and simulate.This paper mainly discusses the mean value principle of a class of fractional neutral stochastic differential equations driven by Lévy noise with impulses.Firstly,the existence and uniqueness of the solution is proved by successive approximation method,and it is obtained that the solution of the averaging equation converges to the solution of the original equation in the sense of mean square and probability.