Abstract This paper is concerned with the existence and uniqueness, the almost sure stability with general decay rate (including almost sure exponential stability, almost sure polynomial stability and almost sure logarithmic stability) for the global solution of nonlinear neutral stochastic functional hybrid differential equations with Levy noise. The key technique used is the method of Lyapunov function, nonnegative semi-martingale convergence theorem and the theory of M-matrix. We use auxiliary functions to dominate the corresponding Lyapunov function and the diffusion operator. Our conditions on the diffusion operator are weaker than those in the related existing works. Finally, one example is given to show the effectiveness of the obtained theory.

中文翻译：

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具有 Lévy 噪声的中性随机泛函混合微分方程的一般衰减率稳定性

摘要 本文研究非线性中性随机泛函混合微分方程的整体解的存在唯一性、一般衰减率的几乎肯定稳定性（包括几乎肯定指数稳定性、几乎肯定多项式稳定性和几乎肯定对数稳定性）。噪音。使用的关键技术是Lyapunov函数方法、非负半鞅收敛定理和M矩阵理论。我们使用辅助函数来支配相应的李雅普诺夫函数和扩散算子。我们对扩散算子的条件比现有相关工作中的条件弱。最后给出一个例子来说明所得理论的有效性。