Lévy驱动的一类分数阶随机微分方程的稳定性

The Stability of a Class Stochastic Fractional Differential Equations Driven by Lévy Noise

文章讨论了一类由Lévy噪声扰动的分数阶中立型随机泛函混杂微分方程解的稳定性,利用Lyapunov泛函、非负半鞅收敛定理以及M-矩阵的理论证明了方程的解在一般衰减速度下的的几乎必然稳定性,并给出了任意状态下各系数的上界。

In this paper, we discuss the stability with general decay rate of neutral stochastic fractional hybrid differential equations driven by Lévy noise. By using Lyapunov function, nonnegative semi-martingale convergence theorem and the theory of M-matrix, we propose sufficient conditions for the almost sure stability. We also give an upper bound of each coefficient at any state.