Abstract Recently, the asymptotic stability for Markov jump stochastic functional differential systems (SFDSs) was studied, whose stability criteria relied on the intervals lengths of continuous delays. Whereas, so far all the existing references require the rigorous global Lipschitz condition for the delay parts of the drift coefficients and do not consider the challenging factors of exponential decay and neutral issue. Motivated by the aforementioned considerations and the advantages of the degenerate functionals, this paper aims to weaken the global Lipschitz condition for the delay parts of the drift coefficients and investigate the delay-dependent exponential stability and asymptotic boundedness for highly nonlinear Markov jump neutral SFDSs with the method of multiple degenerate functionals. Of course, the delay-independent assertions are as well derived here.

中文翻译：

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非线性马尔可夫跳跃中性随机泛函微分系统的稳定性分析

摘要 近年来，研究了马尔可夫跳跃随机泛函微分系统(SFDS)的渐近稳定性，其稳定性准则依赖于连续时滞的区间长度。然而，到目前为止，所有现有参考文献都要求漂移系数的延迟部分具有严格的全局 Lipschitz 条件，并且没有考虑指数衰减和中性问题的挑战性因素。基于上述考虑和退化泛函的优点，本文旨在削弱漂移系数延迟部分的全局 Lipschitz 条件，并研究高度非线性马尔可夫跳跃中性 SFDS 的延迟相关指数稳定性和渐近有界性多重退化泛函的方法。当然，