Exponential stability of implicit numerical solution for nonlinear neutral stochastic differential equations with time-varying delay and poisson jumps
Exponential stability of implicit numerical solution for nonlinear neutral stochastic differential equations with time-varying delay and poisson jumps
复制标题
时变时滞和泊松跳非线性中性随机微分方程隐式数值解的指数稳定性
DOI：
10.1002/mma.7132
复制
发表时间：
2021
影响因子：
2.9
通讯作者：
Zhang Bo
中科院分区：
文献类型：
--
作者：
Mo Haoyi;Liu Linna;Xing Mali;Deng Feiqi;Zhang Bo
本文研究了具有时变时滞和Poisson跳的中立型随机微分方程的指数均方稳定性.当所有的漂移、扩散和跳跃系数都允许是非线性的时，得到了方程解析解的指数均方稳定性。结果表明，在一定的非线性条件下，隐式向后Euler-Maruyama数值解能够再现解析解的稳定性。它不同于显式Euler-Maruyama数值解，后者的稳定性依赖于线性增长条件。在对时滞函数和补偿泊松过程的性质有一定要求的情况下，我们处理了时变时滞和泊松跳。一个高度非线性的例子来证实我们的理论的有效性。
The aim of this work is to investigate the exponential mean‐square stability for neutral stochastic differential equations with time‐varying delay and Poisson jumps. When all the drift, diffusion, and jumps coefficients are allowed to be nonlinear, the exponential mean‐square stability of the analytic solution to the equation is obtained. It is revealed that the implicit backward Euler–Maruyama numerical solution can reproduce the corresponding stability of the analytic solution under some given nonlinear conditions. It is different from the explicit Euler–Maruyama numerical solution whose stability depends on the linear growth condition. With some requirements related to the delayed function and the property of compensated Poisson process, we deal with time‐varying delay and Poisson jumps. One highly nonlinear example is given to confirm the effectiveness of our theory.