Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jump
Stability analysis of the θ-method for hybrid neutral stochastic functional differential equations with jump
复制标题
带跳跃的混合中性随机泛函微分方程α法的稳定性分析
DOI：
10.1016/j.chaos.2021.111062
复制
发表时间：
2021
影响因子：
7.8
通讯作者：
Qigui Yang
中科院分区：
文献类型：
--
作者：
Guangjie Li;Qigui Yang
关于带马尔可夫切换和跳的中立型随机泛函微分方程数值方法的稳定性的结果很少，本文的结果可以丰富这一领域。证明了平凡解的几乎必然指数稳定性和均方指数稳定性。·证明了在适当的条件下，θ -方法能保持平凡解的几乎必然指数稳定性和均方指数稳定性。·利用离散半鞅收敛定理证明了θ -方法的几乎必然指数稳定性，而不需要借助于Borel-Cantelli引理和Chebyshev不等式.关于带跳的混合中立型随机泛函微分方程（也称为带马尔可夫切换和跳的中立型随机泛函微分方程（NSFDEwMJ））的数值方法的稳定性，似乎很少有结果是已知的。本文主要研究NSFDEwMJ的θ -方法的指数稳定性（几乎必然稳定性和均方指数稳定性）。首先证明了NSFDEwMJ的平凡解几乎必然是均方指数稳定的。然后证明了θ -方法可以保持平凡解的相同结论。数值例子说明所得到的结果。
Few results on the stability of numerical methods for the neutral stochastic functional differential equations with Markovian switching and jumps, results obtained in this manuscript can enrich this area. Illustrate the almost sure exponential stability and the mean-square exponential stability of the trivial solution. • Show the θ -method can preserve the almost sure exponential stability and the mean-square exponential stability of the trivial solution under some appropriate condition. • The almost sure exponential stability of the θ -method is obtained by the discrete semi-martingale convergence theorem without resorting to using the Borel-Cantelli lemma and the Chebyshev inequality. Few results seems to be known about the stability of numerical methods for the hybrid neutral stochastic functional differential equations with jumps (also known as the neutral stochastic functional differential equations with Markovian switching and jumps (NSFDEwMJs)). This paper mainly investigates the exponential stability (both the almost sure and the mean-square exponential stability) of the θ -method for NSFDEwMJs. Precisely, it is first illustrated that the trivial solution of the NSFDEwMJ is almost surely and mean-square exponentially stable. It is then shown that the θ -method can preserve the same conclusions of the trivial solution. Numerical examples are demonstrated to illustrate the obtained results.