【摘要】 研究带跳时滞随机微分方程Euler-Maruyama方法的指数稳定性.在全局Lipschitz条件及解析解和数值解在均方有界的条件下,证明SDDEJs的指数稳定性的充要条件是Euler-Maruyama方法下构造的数值解是指数稳定性的.避免寻找Lyapunov函数的困难,将指数稳定性的等价关系推广到带跳情形.更多还原

【Abstract】 The exponential stability of differential equations with stochastic jumping time-delay was studied on the basis of Euler-Maruyama method.It was verified in the case of agreement of global Lipschitz condition and mean square bounded analytic and numeric solutions that the sufficient and necessary condition of SDDEJs exponential stability was the exponential stability of the numeric solution constructed with Fuler-Maruyama method,Thus,the difficulty was avoided in finding the Lyapunov function and the equivalent relationship of exponential stability was generalized to the case with the jumps.更多还原